Daily Papers

Multi-player interactive world models aim to simulate shared environments from multiple players' perspectives, but achieving robust generation while scaling to more players remains challenging. Existing approaches that rely on fully-connected communication (e.g., Solaris) incur quadratic attention costs as the number of players grows, while centralized approaches (e.g., γ-World) suffer from interference between unrelated events in a shared global representation. To address these challenges, we present Multics, a multi-player video generation framework with hierarchical communication that structures information exchange across player, group, and global levels. This hierarchy introduces group tokens into self-attention as intermediate group-level representations that aggregate locally relevant player information. These tokens connect to global tokens for cross-group communication, while the hierarchical topology limits direct mixing between unrelated local events. Group-token parameters are shared across group slots, allowing the same communication module to accommodate varying numbers of players without introducing new group-specific parameters. We further propose budget-constrained dynamic grouping based on recent camera trajectories, which adaptively groups relevant players while limiting unnecessary communication. Experiments demonstrate that Multics achieves state-of-the-art performance in 4- and 6-player settings, with improved cross-player consistency, player-specific action and camera controllability, and interference robustness. Moreover, Multics generalizes from 4-player training to 6-, 8-, and 10-player inference without retraining, while reducing self-attention computation compared with fully-connected communication.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

Current evaluations of Large Language Model (LLM) agents primarily emphasize task completion, often overlooking resource efficiency and adaptability. This neglects a crucial capability: agents' ability to devise and adjust cost-optimal plans in response to changing environments. To bridge this gap, we introduce CostBench, a scalable, cost-centric benchmark designed to evaluate agents' economic reasoning and replanning abilities. Situated in the travel-planning domain, CostBench comprises tasks solvable via multiple sequences of atomic and composite tools with diverse, customizable costs. It also supports four types of dynamic blocking events, such as tool failures and cost changes, to simulate real-world unpredictability and necessitate agents to adapt in real time. Evaluating leading open-sourced and proprietary models on CostBench reveals a substantial gap in cost-aware planning: agents frequently fail to identify cost-optimal solutions in static settings, with even GPT-5 achieving less than 75% exact match rate on the hardest tasks, and performance further dropping by around 40% under dynamic conditions. By diagnosing these weaknesses, CostBench lays the groundwork for developing future agents that are both economically rational and robust.

LLM-based agents show strong potential for long-horizon reasoning, yet their context size is limited by deployment factors (e.g., memory, latency, and cost), yielding a constrained context budget. As interaction histories grow, this induces a trade-off between retaining past information and staying within the context limit. To address this challenge, we propose Budget-Aware Context Management (BACM), which formulates context management as a sequential decision problem with a context budget constraint. It enables agents to assess the available budget before incorporating new observations and decide when and how much of the interaction history to compress. We further develop BACM-RL, an end-to-end curriculum-based reinforcement learning approach that learns compression strategies under varying context budgets. Experiments on compositional multi-objective QA and long-horizon web browsing benchmarks show that BACM-RL consistently outperforms prior methods across model scales and task complexities, achieving over 1.6times gains over strong baselines in high-complexity settings, while maintaining strong advantages as budgets shrink, where most methods exhibit a downward performance trend.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Scaling test-time computation improves performance across different tasks on large language models (LLMs), which has also been extended to tool-augmented agents. For these agents, scaling involves not only "thinking" in tokens but also "acting" via tool calls. The number of tool calls directly bounds the agent's interaction with the external environment. However, we find that simply granting agents a larger tool-call budget fails to improve performance, as they lack "budget awareness" and quickly hit a performance ceiling. To address this, we study how to scale such agents effectively under explicit tool-call budgets, focusing on web search agents. We first introduce the Budget Tracker, a lightweight plug-in that provides the agent with continuous budget awareness, enabling simple yet effective scaling. We further develop BATS (Budget Aware Test-time Scaling), an advanced framework that leverages this awareness to dynamically adapt its planning and verification strategy, deciding whether to "dig deeper" on a promising lead or "pivot" to new paths based on remaining resources. To analyze cost-performance scaling in a controlled manner, we formalize a unified cost metric that jointly accounts for token and tool consumption. We provide the first systematic study on budget-constrained agents, showing that budget-aware methods produce more favorable scaling curves and push the cost-performance Pareto frontier. Our work offers empirical insights toward a more transparent and principled understanding of scaling in tool-augmented agents.

Memory is increasingly central to Large Language Model (LLM) agents operating beyond a single context window, yet most existing systems rely on offline, query-agnostic memory construction that can be inefficient and may discard query-critical information. Although runtime memory utilization is a natural alternative, prior work often incurs substantial overhead and offers limited explicit control over the performance-cost trade-off. In this work, we present BudgetMem, a runtime agent memory framework for explicit, query-aware performance-cost control. BudgetMem structures memory processing as a set of memory modules, each offered in three budget tiers (i.e., Low/Mid/High). A lightweight router performs budget-tier routing across modules to balance task performance and memory construction cost, which is implemented as a compact neural policy trained with reinforcement learning. Using BudgetMem as a unified testbed, we study three complementary strategies for realizing budget tiers: implementation (method complexity), reasoning (inference behavior), and capacity (module model size). Across LoCoMo, LongMemEval, and HotpotQA, BudgetMem surpasses strong baselines when performance is prioritized (i.e., high-budget setting), and delivers better accuracy-cost frontiers under tighter budgets. Moreover, our analysis disentangles the strengths and weaknesses of different tiering strategies, clarifying when each axis delivers the most favorable trade-offs under varying budget regimes.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BBAM (Bayesian Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the E^3 metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BBAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to +70% accuracy gains, -39% token reduction, and +187.5% improvement in E^3. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B)-demonstrating Plan-and-Budget's ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

Agentic systems increasingly solve complex user requests by executing orchestrated workflows, where subtasks are assigned to specialized models or tools and coordinated according to their dependencies. While recent work improves agent efficiency by optimizing the performance--cost--latency frontier, real deployments often impose concrete requirements: a workflow must be completed within a specified budget and before a specified deadline. This shifts the goal from average efficiency optimization to maximizing the probability that the entire workflow completes successfully under explicit budget and deadline constraints. We study constraint-driven online resource allocation for agentic workflows. Given a dependency-structured workflow and estimates of success rates and generation lengths for each subtask--model pair, the executor allocates models and parallel samples across simultaneously executable subtasks while managing the remaining budget and time. We formulate this setting as a finite-horizon stochastic online allocation problem and propose Monte Carlo Portfolio Planning (MCPP), a lightweight closed-loop planner that directly estimates constrained completion probability through simulated workflow executions and replans after observed outcomes. Experiments on CodeFlow and ProofFlow demonstrate that MCPP consistently improves constrained completion probability over strong baselines across a wide range of budget--deadline constraints.

Large language models (LLMs) can achieve strong reasoning performance with sufficient computation, but they do not inherently know how much computation a task requires. We study budgeted inference-time reasoning for multiple tasks under a strict global token constraint and formalize it as a Ordered Stochastic Multiple-Choice Knapsack Problem(OS-MCKP). This perspective highlights a meta-cognitive requirement -- anticipating task difficulty, estimating return over investment (ROI), and allocating computation strategically. We propose ROI-Reasoning, a two-stage framework that endows LLMs with intrinsic, budget-aware rationality. In the first stage, Meta-Cognitive Fine-Tuning teaches models to predict reasoning cost and expected utility before generation, enabling explicit solve-or-skip decisions. Next, Rationality-Aware Reinforcement Learning optimizes sequential decision making under a hard token budget, allowing models to learn long-horizon allocation strategies. Across budgeted mathematical reasoning benchmarks, ROI-Reasoning consistently improves overall score while substantially reducing regret under tight computation budgets.

Test-time scaling has become a dominant paradigm for improving LLM agent reliability, yet current approaches treat compute as an abundant resource, allowing agents to exhaust token and tool budgets on redundant steps or dead-end trajectories. Existing budget-aware methods either require expensive fine-tuning or rely on coarse, trajectory-level heuristics that cannot intervene mid-execution. We propose the Budget-Aware Value Tree (BAVT), a training-free inference-time framework that models multi-hop reasoning as a dynamic search tree guided by step-level value estimation within a single LLM backbone. Another key innovation is a budget-conditioned node selection mechanism that uses the remaining resource ratio as a natural scaling exponent over node values, providing a principled, parameter-free transition from broad exploration to greedy exploitation as the budget depletes. To combat the well-known overconfidence of LLM self-evaluation, BAVT employs a residual value predictor that scores relative progress rather than absolute state quality, enabling reliable pruning of uninformative or redundant tool calls. We further provide a theoretical convergence guarantee, proving that BAVT reaches a terminal answer with probability at least 1-ε under an explicit finite budget bound. Extensive evaluations on four multi-hop QA benchmarks across two model families demonstrate that BAVT consistently outperforms parallel sampling baselines. Most notably, BAVT under strict low-budget constraints surpasses baseline performance at 4times the resource allocation, establishing that intelligent budget management fundamentally outperforms brute-force compute scaling.

Moving ML-mediated decision making onto privacy-preserving clients decentralises the economic decision along with the inference. Shared budget constraints then depend on information that cannot be globally current, creating an information-structure failure that conventional pacing is not designed to solve. We study this information misalignment in an auction-logic-faithful on-device simulation with 36 campaigns and 50 devices. Accounting is in dimensionless integer score units; no currency semantics are claimed. Across 30 paired demand paths, proportional Even pacing overspends 17.77% after one tick of staleness and 1,669.31% after 50 ticks under the original 20-times budget pressure. The effect does not depend on that severe a budget: at two-times pressure, 50-tick overspend remains 106.95%. A visible-budget no-sale guard makes zero-lag compliance exact at this score-unit granularity, yet leaves 11.88% overspend at one tick because other devices' debits remain invisible. A declared bursty, heterogeneous-device sweep retains a strictly increasing mean lag curve. We derive a finite-window expected excess-debit bound under conditional charge caps and find positive paired slack in every bounded-value cell. A second, incentive misalignment arises when the ML/pacing score transformation is allowed to change payment units: 98.23% of rival auctions at one tick admit a profitable deviation. An executable implementation-level counterexample isolates the runner-up's multiplier in the winner's price. Critical-base-bid payment is per-auction DSIC conditional on current multipliers, but does not establish dynamic truthfulness and does not repair base-value ranking disagreement.

As large language models (LLMs) evolve into autonomous agents that execute long-horizon workflows, invoking a high-capability model at every step becomes economically unsustainable. While model routing is effective for single-turn queries, agentic routing is a sequential, path-dependent problem: early mistakes compound, feedback is often at the end of the episode, and deployments often demand strict per-task spending limits. We propose Budget-Aware Agentic Routing, which selects between a cheap and an expensive model at each step to optimize the cost--success frontier and to operate under strict per-task budgets. We propose Boundary-Guided Training, which leverages two boundary policies (always-small vs.\ always-large) to build a difficulty taxonomy and to anchor learning under sparse rewards. Our approach warms start with boundary-guided SFT data synthesis via stratified sampling of cost-efficient trajectories, then applies Boundary-Guided Policy Optimization (BoPO), combining boundary-relative rewards with a reference-guided advantage to avoid degenerate cheap-failure solutions. Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost while demonstrating generalization to strict inference-time budget constraints. Overall, our work establishes a foundational framework for agentic routing, shifting the paradigm from static model selection to dynamic, budget-aware sequential decision-making.

We study budget-constrained tool-augmented agents, where a large language model must solve multi-step tasks by invoking external tools under a strict monetary budget. We formalize this setting as sequential decision making in context space with priced and stochastic tool executions, making direct planning intractable due to massive state-action spaces, high variance of outcomes and prohibitive exploration cost. To address these challenges, we propose INTENT, an inference-time planning framework that leverages an intention-aware hierarchical world model to anticipate future tool usage, risk-calibrated cost, and guide decisions online. Across cost-augmented StableToolBench, INTENT strictly enforces hard budget feasibility while substantially improving task success over baselines, and remains robust under dynamic market shifts such as tool price changes and varying budgets.

Reinforcement learning (RL) is the dominant paradigm for post-training large language models. However, in the online, on-policy setting, rollout generation dominates the computational cost of training. Group-based policy optimization methods compute advantages from multiple rollouts per prompt, yet they indiscriminately allocate budget to prompts with collapsed reward distributions, wasting expensive rollouts on negligible learning signals. We demonstrate that group-based updates are most effective in regimes of high reward variance. Since the policy evolves throughout training, prompt informativeness must be estimated online rather than precomputed, but exhaustively evaluating every prompt is computationally prohibitive. We introduce Pilot-Commit, a budget-aware rollout allocation framework for group-based RL post-training. Pilot-Commit decouples prompt evaluation from exploitation: a pilot stage estimates per-prompt informativeness using a fraction of the budget, and the remaining rollouts are allocated to high-leverage prompts while low-signal prompts are skipped. Across multiple math reasoning benchmarks and model scales from 1.5B to 14B parameters, Pilot-Commit matches baseline accuracy with significantly lower sampling costs, reaching target accuracy up to 1.9times faster than GRPO and 4.0times faster than DAPO in cumulative rollouts.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Large reasoning models achieve remarkable performance through extensive chain-of-thought generation, yet exhibit significant computational inefficiency by applying uniform reasoning strategies regardless of problem complexity. We present Hierarchical Budget Policy Optimization (HBPO), a reinforcement learning framework that enables models to learn problem-specific reasoning depths without sacrificing capability. HBPO addresses the fundamental challenge of exploration space collapse in efficiency-oriented training, where penalties on long output length systematically bias models away from necessary long reasoning paths. Through hierarchical budget exploration, our approach partitions rollout samples into multiple subgroups with distinct token budgets, aiming to enable efficient resource allocation while preventing degradation of capability. We introduce differentiated reward mechanisms that create budget-aware incentives aligned with the complexity of the problem, allowing models to discover natural correspondences between task requirements and computational effort. Extensive experiments demonstrate that HBPO reduces average token usage by up to 60.6% while improving accuracy by 3.14% across four reasoning benchmarks. Unlike existing methods that impose external constraints or rely on discrete mode selection, HBPO exhibits emergent adaptive behavior where models automatically adjust reasoning depth based on problem complexity. Our results suggest that reasoning efficiency and capability are not inherently conflicting, and can be simultaneously optimized through appropriately structured hierarchical training that preserves exploration diversity.

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.

The k-Means clustering problem on n points is NP-Hard for any dimension dge 2, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an O(kn^2) time dynamic programming algorithm that uses O(kn) space. It turns out that the problem has been considered under a different name more than twenty years ago. We present all the existing work that had been overlooked and compare the various solutions theoretically. Moreover, we show how to reduce the space usage for some of them, as well as generalize them to data structures that can quickly report an optimal k-Means clustering for any k. Finally we also generalize all the algorithms to work for the absolute distance and to work for any Bregman Divergence. We complement our theoretical contributions by experiments that compare the practical performance of the various algorithms.

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

The expanding computational costs and limited resources underscore the critical need for budgeted-iteration training, which aims to achieve optimal learning within predetermined iteration budgets.While learning rate schedules fundamentally govern the performance of different networks and tasks, particularly in budgeted-iteration scenarios, their design remains largely heuristic, lacking theoretical foundations.In addition, the optimal learning rate schedule requires extensive trial-and-error selection, making the training process inefficient.In this work, we propose the Unified Budget-Aware (UBA) schedule, a theoretically grounded learning rate schedule that consistently outperforms commonly-used schedules among diverse architectures and tasks under different constrained training budgets.First, we bridge the gap by constructing a novel training budget-aware optimization framework, which explicitly accounts for the robustness to landscape curvature variations.From this framework, we derive the UBA schedule, controlled by a single hyper-parameter varphi that provides a trade-off between flexibility and simplicity, eliminating the need for per-network numerical optimization. Moreover, we establish a theoretical connection between varphi and the condition number, adding interpretation and justification to our approach. Besides, we prove the convergence for different values of varphi.We offer practical guidelines for its selection via theoretical analysis and empirical results.xtensive experimental results show that UBA consistently surpasses the commonly-used schedules across diverse vision and language tasks, spanning network architectures (e.g., ResNet, OLMo) and scales, under different training-iteration budgets.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

In cognitive science, resource rationality asks how an agent should allocate limited computation to maximize expected value. Most reasoning and agent benchmarks use independent per-task budgets; existing shared-budget studies do not calibrate suite performance against the same model's demonstrated single-problem competence. We introduce R^3-Bench, which evaluates six-problem suites under shared budgets across mathematics, competitive programming, and abstract reasoning in tool-free and agentic settings. Matched single-problem response curves define an offline empirical oracle over observed successes. Across 72 main-table cells for six models, the oracle mean matches or exceeds the contest mean in all cells and is strictly higher in 71. Under moderate tool-free pressure, equal-allocation replay also exceeds contest performance for four of six models. Trajectory diagnostics reveal limited strategy updating and pressure-dependent failure patterns. In a three-model diagnostic under strong agentic pressure, at least one fixed scheduler exceeds the contest mean in six of nine cells, but no policy dominates across domains. These results expose a persistent gap between demonstrated competence and shared-budget realization.

LLM-powered coding agents, which operate in iterative loops (turns) to solve software engineering tasks, are becoming increasingly powerful. However, their practical deployment is hindered by significant and unpredictable costs. This challenge arises from a combination of factors: quadratically growing token counts with each turn, the high price of models, the large number of turns required for real-world tasks, and the tendency of agents to take inefficient or unnecessary actions. While existing research focuses on optimizing individual turns, the strategic control of the total number of turns remains an underexplored area for managing agent performance and cost. To address this gap, we conduct a comprehensive empirical study on SWE-bench using three state-of-the-art models and evaluate the impact of three distinct turn-control strategies: an unrestricted baseline, a fixed-turn limit with reminders, and a novel dynamic-turn strategy that grants extensions on-demand. Our findings first reveal a fundamental trade-off in the unrestricted setting, where no single model excels across performance, cost, and turn efficiency. We then show that a fixed-turn limit, specifically at the 75th percentile of the baseline, serves as a "sweet spot", substantially reducing costs (by 24%-68%) with minimal impact on solve rates. Most significantly, the dynamic-turn strategy consistently outperforms fixed-limit approaches, achieving comparable or better solve rates while further reducing costs by an additional 12%-24% by intelligently allocating resources only to tasks that need them. This work provides the first systematic analysis of turn-control strategies, offering simple yet effective guidelines for developers to balance cost and efficacy. We demonstrate that dynamic resource allocation is a superior, easy-to-implement approach for deploying powerful yet economically viable coding agents.

Online display advertising platforms service numerous advertisers by providing real-time bidding (RTB) for the scale of billions of ad requests every day. The bidding strategy handles ad requests cross multiple channels to maximize the number of clicks under the set financial constraints, i.e., total budget and cost-per-click (CPC), etc. Different from existing works mainly focusing on single channel bidding, we explicitly consider cross-channel constrained bidding with budget allocation. Specifically, we propose a hierarchical offline deep reinforcement learning (DRL) framework called ``HiBid'', consisted of a high-level planner equipped with auxiliary loss for non-competitive budget allocation, and a data augmentation enhanced low-level executor for adaptive bidding strategy in response to allocated budgets. Additionally, a CPC-guided action selection mechanism is introduced to satisfy the cross-channel CPC constraint. Through extensive experiments on both the large-scale log data and online A/B testing, we confirm that HiBid outperforms six baselines in terms of the number of clicks, CPC satisfactory ratio, and return-on-investment (ROI). We also deploy HiBid on Meituan advertising platform to already service tens of thousands of advertisers every day.

We utilize an offline reinforcement learning (RL) model for sequential targeted promotion in the presence of budget constraints in a real-world business environment. In our application, the mobile app aims to boost customer retention by sending cash bonuses to customers and control the costs of such cash bonuses during each time period. To achieve the multi-task goal, we propose the Budget Constrained Reinforcement Learning for Sequential Promotion (BCRLSP) framework to determine the value of cash bonuses to be sent to users. We first find out the target policy and the associated Q-values that maximizes the user retention rate using an RL model. A linear programming (LP) model is then added to satisfy the constraints of promotion costs. We solve the LP problem by maximizing the Q-values of actions learned from the RL model given the budget constraints. During deployment, we combine the offline RL model with the LP model to generate a robust policy under the budget constraints. Using both online and offline experiments, we demonstrate the efficacy of our approach by showing that BCRLSP achieves a higher long-term customer retention rate and a lower cost than various baselines. Taking advantage of the near real-time cost control method, the proposed framework can easily adapt to data with a noisy behavioral policy and/or meet flexible budget constraints.

Budget-constrained agentic search arises when an LLM agent must refine candidates under a small evaluation budget, because validation is expensive, generation requires multiple model calls, or both. In this regime, standard MCTS allocates budget poorly: exploration bonuses dominate at low visit counts, unpromising siblings are expanded before promising chains can deepen, and branching is independent of node quality. We introduce ExTS, a tree-search policy that treats expansion itself as a value-of-information decision. ExTS combines three mechanisms: discriminative reward shaping to separate candidates under narrow score distributions, a stochastic virtual child that estimates the value of creating a new branch from the parent's reward history, and quality-conditioned branching that expands only when a node's score justifies the budget cost. Across prompt optimization, code generation, molecular structure elucidation, and agentic workflow optimization, ExTS is competitive with or improves over task-specific tree-search baselines, with an average relative gain of +5.5% using a single fixed configuration. We further introduce pilot-run diagnostics that characterize what makes budget-constrained agentic search problems structurally different from one another, providing both understanding of the problem space and practical guidance for adaptation.

Most image generation models rely on uniform tokenization, allocating the exact same computational budget to equally-sized image patches. This static paradigm cannot adapt to different resource constraints at inference time, and yields suboptimal quality-cost tradeoff by devoting the same effort to both plain backgrounds and intricate details. We propose BudgetPix, an adaptive tokenization framework that dynamically allocates compute based on visual complexity and spatial layout, enabling flexible computational budgeting at inference time. BudgetPix comprises three key components: (1) an adaptive encoder that maps a fixed-size image to a variable-length token sequence using an entropy-guided quadtree alongside a multi-scale patch embedder; (2) a scale-aware decoder reconstructs fixed-resolution images from multi-scale token sets; and (3) a flexible training and sampling schedule that enables pixel-space denoisers to operate across variable token counts. BudgetPix seamlessly integrates with existing pixel-space diffusion architectures, enabling a single checkpoint to be operated at a wide range of compute budgets. Evaluated on text-to-image generation, BudgetPix matches the fidelity of MiniT2I-L at 512^2 and PixelDiT at 1024^2 using just 25% of the original compute budget. In class-conditional generation using a MeanFlow backbone, BudgetPix requires merely 60% of the full compute budget to produce images with near-zero quality degradation, observing a marginal 0.8-point increase in FID. Comprehensive assessments by human and VLM judges confirm that BudgetPix establishes a significantly improved quality-efficiency tradeoff over prior budget-adaptive baselines. More details are available at our project page: https://karaozgur.com/BudgetPix

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this paper, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover the dual sub-gradient descent and dual multiplicative weights update algorithm. The resulting algorithms are simple, fast, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. We discuss applications to network revenue management, online bidding in repeated auctions with budget constraints, online proportional matching with high entropy, and personalized assortment optimization with limited inventory.

Demystifying the interactions among multiple agents from their past trajectories is fundamental to precise and interpretable trajectory prediction. However, previous works mainly consider static, pair-wise interactions with limited relational reasoning. To promote more comprehensive interaction modeling and relational reasoning, we propose DynGroupNet, a dynamic-group-aware network, which can i) model time-varying interactions in highly dynamic scenes; ii) capture both pair-wise and group-wise interactions; and iii) reason both interaction strength and category without direct supervision. Based on DynGroupNet, we further design a prediction system to forecast socially plausible trajectories with dynamic relational reasoning. The proposed prediction system leverages the Gaussian mixture model, multiple sampling and prediction refinement to promote prediction diversity, training stability and trajectory smoothness, respectively. Extensive experiments show that: 1)DynGroupNet can capture time-varying group behaviors, infer time-varying interaction category and interaction strength during trajectory prediction without any relation supervision on physical simulation datasets; 2)DynGroupNet outperforms the state-of-the-art trajectory prediction methods by a significant improvement of 22.6%/28.0%, 26.9%/34.9%, 5.1%/13.0% in ADE/FDE on the NBA, NFL Football and SDD datasets and achieve the state-of-the-art performance on the ETH-UCY dataset.

Reasoning is critical for large language models (LLMs) to excel in a wide range of tasks. While methods like Chain-of-Thought (CoT) reasoning enhance LLM performance by decomposing problems into intermediate steps, they also incur significant overhead in token usage, leading to increased costs. We find that the reasoning process of current LLMs is unnecessarily lengthy and it can be compressed by including a reasonable token budget in the prompt, but the choice of token budget plays a crucial role in the actual compression effectiveness. We then propose a token-budget-aware LLM reasoning framework, which dynamically estimates token budgets for different problems based on reasoning complexity and uses the estimated token budgets to guide the reasoning process. Experiments show that our method effectively reduces token costs in CoT reasoning with only a slight performance reduction, offering a practical solution to balance efficiency and accuracy in LLM reasoning. Code: https://github.com/GeniusHTX/TALE.

While long Chain-of-Thought (CoT) distillation effectively transfers reasoning capability to smaller language models, the reasoning process often remains redundant and computational budget uncontrollable, leading to inefficient resource usage. To address this limitation, we propose Budget-Aware Reasoning Distillation (BARD), a novel framework that simultaneously distills reasoning capability and enables fine-grained control over the reasoning length. BARD uses the thinking budget as a user-specified control signal, allowing the model to dynamically balance reasoning performance and computational efficiency. To achieve this concept, BARD introduces a two-phase training regimen. The first phase, Supervised Fine-Tuning (SFT) on teacher-generated long CoT data compressed to various budget levels, bootstrapping the model's understanding of budget constraints. The second phase leverages Reinforcement Learning (RL) from a reward signal in consideration of reasoning performance and budget fidelity simultaneously. Incorporating the two-phase regimen is crucial to avoiding policy degradation and ensuring that both objectives are optimized jointly. Extensive experiments demonstrate that our method empowers an 8B student model to achieve strong performance on challenging reasoning benchmarks (AIME24, AIME25, GPQA) while providing precise and adaptive control over its reasoning length across a wide range of budgets.

Reasoning language models increasingly use test-time compute to improve performance, but existing evaluations typically study this compute one question at a time. Yet when multiple problems share an end-to-end cost or latency constraint, models must decide how to divide limited inference compute among them. We introduce an exam-style evaluation framework for studying this setting, in which a model must distribute one shared token budget across questions with different difficulty and point values to maximize its total score. Across several open and frontier reasoning models, we find that models fail to allocate a shared budget strategically across questions of varying difficulties and values. Models behave largely as greedy sequential solvers: they prioritize questions by presentation order, front-load effort on early questions, and remain insensitive to value, with these tendencies becoming more pronounced as the number of questions grows. Explicit planning prompts spread compute more evenly but do not produce value- or difficulty-aware prioritization. The same behavioral pattern extends from mathematical to code reasoning. These findings establish global budget allocation as a distinct capability that is not captured by conventional per-question evaluation and remains a challenge for current reasoning models.

While LLMs excel at open-ended reasoning, they often struggle with cost-sensitive planning, either treating all actions as having equal cost or failing to stay within strict budgets. In this paper, we introduce Cost-Augmented Monte Carlo Tree Search (CATS), a novel approach that brings explicit cost-awareness into LLM-guided planning. Tight cost constraints push the planner to quickly identify infeasible solutions, while looser constraints encourage optimization for minimal cost. We benchmark top LLMs such as GPT-4.1, Claude-3.7-Sonnet, and DeepSeek-R1, against our CATS planner to evaluate their performance in cost-sensitive scenarios. Our experiments suggest that raw LLMs such as GPT-4.1 often falter under tight budgets, whereas CATS consistently delivers strong performance, achieving higher task success rates and better cost efficiency. CATS provides an effective solution for budget-aware decision-making by combining the reasoning power of LLMs with structured search.

Assessing the capabilities and risks of frontier AI systems is a critical area of research, and recent work has shown that repeated sampling from models can dramatically increase both. For instance, repeated sampling has been shown to increase their capabilities, such as solving difficult math and coding problems, but it has also been shown to increase their potential for harm, such as being jailbroken. Such results raise a crucial question for both capability and safety forecasting: how can one accurately predict a model's behavior when scaled to a massive number of attempts, given a vastly smaller sampling budget? This question is directly relevant to model providers, who serve hundreds of millions of users daily, and to governmental regulators, who seek to prevent harms. To answer this questions, we make three contributions. First, we find that standard methods for fitting these laws suffer from statistical shortcomings that hinder predictive accuracy, especially in data-limited scenarios. Second, we remedy these shortcomings by introducing a robust estimation framework, which uses a beta-binomial distribution to generate more accurate predictions from limited data. Third, we propose a dynamic sampling strategy that allocates a greater budget to harder problems. Combined, these innovations enable more reliable prediction of rare risks and capabilities at a fraction of the computational cost.

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

Aiming at promoting the safe real-world deployment of Reinforcement Learning (RL), research on safe RL has made significant progress in recent years. However, most existing works in the literature still focus on the online setting where risky violations of the safety budget are likely to be incurred during training. Besides, in many real-world applications, the learned policy is required to respond to dynamically determined safety budgets (i.e., constraint threshold) in real time. In this paper, we target at the above real-time budget constraint problem under the offline setting, and propose Trajectory-based REal-time Budget Inference (TREBI) as a novel solution that approaches this problem from the perspective of trajectory distribution. Theoretically, we prove an error bound of the estimation on the episodic reward and cost under the offline setting and thus provide a performance guarantee for TREBI. Empirical results on a wide range of simulation tasks and a real-world large-scale advertising application demonstrate the capability of TREBI in solving real-time budget constraint problems under offline settings.

LLM search agents increasingly rely on tools at inference time, but their trajectories are often constrained by hard limits on both tool calls and generated tokens. Under such dual budgets, better answers require not only stronger models, but also explicit control over which search action should receive the next budget unit and when the accumulated evidence is sufficient to commit a final answer. We study this problem in multi-hop question answering (QA) and formulate it as two-stage inference-time budget control. At search time, our controller assigns each feasible action a task-level Value-of-Information (VOI) score, defined as an operational estimate of marginal task value per unit budget under the current search state and remaining dual budget, and uses this score to choose among retrieval, decomposition, and answer commitment. After search, a selective evidence-grounded finalizer compares the trajectory answer with a refined candidate and rewrites only when the residual error appears to be a low-risk answer-form error. Across four multi-hop QA benchmarks, three LLM backbones, and four budget levels, the method yields positive aggregate gains over four audited baselines under the same hard dual-budget protocol. Ablations show that search-time budget control, especially budget-dependent penalty, provides the main performance gain, while answer-time control helps mainly when the retrieval path is already adequate. These results suggest that inference-time budget control for LLM search agents should govern both how budget is spent during search and how the final answer is committed.

Multi-turn LLM serving accumulates dialogue history whose Key-Value (KV) cache grows with every turn and every user, quickly exceeding the model weights themselves and making memory -- not compute -- the binding constraint on throughput. Non-uniform KV compression, which allocates heterogeneous budgets across attention heads, preserves accuracy far better than uniform schemes, yet remains impractical: modern serving stacks assume identical KV lengths across heads, so heterogeneity traps freed memory as page fragmentation, spends up to 25% of prefill time reclaiming scattered pages, and skews GPU workloads that inflate decode latency by up to 1.7times or burn 15--20% of each decode step on re-planning. We observe that this heterogeneity need not be discovered at runtime: head-wise retention follows a two-level structural regularity -- an input-invariant head ranking with narrowly bounded per-head ratios -- that can be calibrated offline from as few as 50 samples. Building on this insight, we present Tangram, a serving framework that statically resolves what prior systems handle dynamically: Budget Reservation fixes each head's post-compression footprint at scheduling time, eliminating page reclamation; Ragged Paging clusters similar-budget heads into independent page tables, turning fragmentation into reclaimable memory; and Ahead-of-Time Load Balancing precomputes balanced GPU partitions with zero runtime planning. Implemented on vLLM, Tangram serves as a drop-in substrate for existing non-uniform compression methods, matching their accuracy while improving end-to-end throughput by up to 2.6times over the full-KV baseline. Our implementation is publicly available at https://github.com/aiha-lab/TANGRAM.

The majority of online display ads are served through real-time bidding (RTB) --- each ad display impression is auctioned off in real-time when it is just being generated from a user visit. To place an ad automatically and optimally, it is critical for advertisers to devise a learning algorithm to cleverly bid an ad impression in real-time. Most previous works consider the bid decision as a static optimization problem of either treating the value of each impression independently or setting a bid price to each segment of ad volume. However, the bidding for a given ad campaign would repeatedly happen during its life span before the budget runs out. As such, each bid is strategically correlated by the constrained budget and the overall effectiveness of the campaign (e.g., the rewards from generated clicks), which is only observed after the campaign has completed. Thus, it is of great interest to devise an optimal bidding strategy sequentially so that the campaign budget can be dynamically allocated across all the available impressions on the basis of both the immediate and future rewards. In this paper, we formulate the bid decision process as a reinforcement learning problem, where the state space is represented by the auction information and the campaign's real-time parameters, while an action is the bid price to set. By modeling the state transition via auction competition, we build a Markov Decision Process framework for learning the optimal bidding policy to optimize the advertising performance in the dynamic real-time bidding environment. Furthermore, the scalability problem from the large real-world auction volume and campaign budget is well handled by state value approximation using neural networks.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

Recent advancements in Large Language Models (LLMs) have leveraged increased test-time computation to enhance reasoning capabilities, a strategy that, while effective, incurs significant latency and resource costs, limiting their applicability in real-world time-constrained or cost-sensitive scenarios. This paper introduces BudgetThinker, a novel framework designed to empower LLMs with budget-aware reasoning, enabling precise control over the length of their thought processes. We propose a methodology that periodically inserts special control tokens during inference to continuously inform the model of its remaining token budget. This approach is coupled with a comprehensive two-stage training pipeline, beginning with Supervised Fine-Tuning (SFT) to familiarize the model with budget constraints, followed by a curriculum-based Reinforcement Learning (RL) phase that utilizes a length-aware reward function to optimize for both accuracy and budget adherence. We demonstrate that BudgetThinker significantly surpasses strong baselines in maintaining performance across a variety of reasoning budgets on challenging mathematical benchmarks. Our method provides a scalable and effective solution for developing efficient and controllable LLM reasoning, making advanced models more practical for deployment in resource-constrained and real-time environments.

Multi-head attention enables Transformers to capture diverse representations, but all attention heads are typically activated for every input, regardless of task complexity. For coarse-grained tasks such as text classification, where relevant information is often global, this fixed allocation can introduce unnecessary computation. We propose BudgetFormer, a Transformer architecture that dynamically allocates attention heads on a per-input basis. The model learns both a head budget and a relevance distribution to select the most informative heads. To support effective head selection, we introduce a training strategy that balances exploration and exploitation. Experiments on text classification tasks show that BudgetFormer reduces FLOPs and memory usage while matching or surpassing the performance of standard multi-head attention. These results highlight adaptive head allocation as an effective approach to improving Transformer efficiency and performance.

While Dynamic Convolution (DY-Conv) has shown promising performance by enabling adaptive weight selection through multiple parallel weights combined with an attention mechanism, the frequency response of these weights tends to exhibit high similarity, resulting in high parameter costs but limited adaptability. In this work, we introduce Frequency Dynamic Convolution (FDConv), a novel approach that mitigates these limitations by learning a fixed parameter budget in the Fourier domain. FDConv divides this budget into frequency-based groups with disjoint Fourier indices, enabling the construction of frequency-diverse weights without increasing the parameter cost. To further enhance adaptability, we propose Kernel Spatial Modulation (KSM) and Frequency Band Modulation (FBM). KSM dynamically adjusts the frequency response of each filter at the spatial level, while FBM decomposes weights into distinct frequency bands in the frequency domain and modulates them dynamically based on local content. Extensive experiments on object detection, segmentation, and classification validate the effectiveness of FDConv. We demonstrate that when applied to ResNet-50, FDConv achieves superior performance with a modest increase of +3.6M parameters, outperforming previous methods that require substantial increases in parameter budgets (e.g., CondConv +90M, KW +76.5M). Moreover, FDConv seamlessly integrates into a variety of architectures, including ConvNeXt, Swin-Transformer, offering a flexible and efficient solution for modern vision tasks. The code is made publicly available at https://github.com/Linwei-Chen/FDConv.

In various work contexts, such as meeting scheduling, collaborating, and project planning, collective decision-making is essential but often challenging due to diverse individual preferences, varying work focuses, and power dynamics among members. To address this, we propose a system leveraging Large Language Models (LLMs) to facilitate group decision-making by managing conversations and balancing preferences among individuals. Our system aims to extract individual preferences from each member's conversation with the system and suggest options that satisfy the preferences of the members. We specifically apply this system to corporate meeting scheduling. We create synthetic employee profiles and simulate conversations at scale, leveraging LLMs to evaluate the system performance as a novel approach to conducting a user study. Our results indicate efficient coordination with reduced interactions between the members and the LLM-based system. The system refines and improves its proposed options over time, ensuring that many of the members' individual preferences are satisfied in an equitable way. Finally, we conduct a survey study involving human participants to assess our system's ability to aggregate preferences and reasoning about them. Our findings show that the system exhibits strong performance in both dimensions.

Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential to automate this process. However, DP problems pose unique challenges due to their inherently stochastic transitions and the limited availability of training data. These factors make it difficult to directly apply existing LLM-based models or frameworks developed for other optimization problems, such as linear or integer programming. We introduce DP-Bench, the first benchmark covering a wide range of textbook-level DP problems to enable systematic evaluation. We present Dynamic Programming Language Model (DPLM), a 7B-parameter specialized model that achieves performance comparable to state-of-the-art LLMs like OpenAI's o1 and DeepSeek-R1, and surpasses them on hard problems. Central to DPLM's effectiveness is DualReflect, our novel synthetic data generation pipeline, designed to scale up training data from a limited set of initial examples. DualReflect combines forward generation for diversity and backward generation for reliability. Our results reveal a key insight: backward generation is favored in low-data regimes for its strong correctness guarantees, while forward generation, though lacking such guarantees, becomes increasingly valuable at scale for introducing diverse formulations. This trade-off highlights the complementary strengths of both approaches and the importance of combining them.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases--thinking and solution--with independently allocated budgets. At test time, Elastic Reasoning prioritize that completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale.

Recent advancements in slow thinking reasoning models have shown exceptional performance in complex reasoning tasks. However, these models often exhibit overthinking (generating redundant reasoning steps for simple problems), leading to excessive computational resource usage. While current mitigation strategies uniformly reduce reasoning tokens, they risk degrading performance on challenging tasks that require extended reasoning. This paper introduces Difficulty-Adaptive Slow Thinking (DAST), a novel framework that enables models to autonomously adjust the length of Chain-of-Thought (CoT) based on problem difficulty. We first propose a Token Length Budget (TLB) metric to quantify difficulty, then leverage budget-aware reward shaping and budget preference optimization to implement DAST. DAST penalizes overlong responses for simple tasks while incentivizing sufficient reasoning for complex problems. Experiments on diverse datasets and model scales demonstrate that DAST effectively mitigates overthinking (reducing token usage by over 30\% on average) while preserving reasoning accuracy on complex problems. Our codes and models are available at https://github.com/AnonymousUser0520/AnonymousRepo01.

Multi-agent LLM systems are often expected to improve as team size increases, yet the scaling behavior may depend on task structure. Our central contribution is to introduce Steiner's taxonomy of group tasks as a framework for analyzing multi-agent LLM scaling and focusing the analysis on disjunctive and compensatory tasks. We model independently sampled agents as conditionally independent given the item, which yields their large-team limits: plurality voting converges to the model's modal answer, and averaging converges to the model's item-level bias. Across selected representative benchmarks, 13 open-weight models, and teams of up to 30 agents, we find qualitatively different scaling behavior. On disjunctive tasks, the probability that at least one agent is correct grows by 5-20 points with team size, but plurality voting over agents that answer directly realises almost none of this potential, as the model predicts to within 0.5 points on average. Multi-round revision raises accuracy considerably, yet the gain is nearly the same with one peer as with 29. In contrast, scaling provides little benefit on Fermi estimation, despite its natural suitability for aggregation: item-level biases shared across the samples of a model account for about 87% of the squared error, so averaging reduces error by only about 6%. Combining model families helps on Fermi estimation but does not surpass the strongest member on disjunctive tasks. These results show that task structure, together with the mechanism combining member outputs, is a fundamental determinant of team scaling.

Cache partitioning techniques have been successfully adopted to mitigate interference among concurrently executing real-time tasks on multi-core processors. Considering that the execution time of a cache-sensitive task strongly depends on the cache available for it to use, co-optimizing cache partitioning and task allocation improves the system's schedulability. In this paper, we propose a hybrid multi-layer design space exploration technique to solve this multi-resource management problem. We explore the interplay between cache partitioning and schedulability by systematically interleaving three optimization layers, viz., (i) in the outer layer, we perform a breadth-first search combined with proactive pruning for cache partitioning; (ii) in the middle layer, we exploit a first-fit heuristic for allocating tasks to cores; and (iii) in the inner layer, we use the well-known recurrence relation for the schedulability analysis of non-preemptive fixed-priority (NP-FP) tasks in a uniprocessor setting. Although our focus is on NP-FP scheduling, we evaluate the flexibility of our framework in supporting different scheduling policies (NP-EDF, P-EDF) by plugging in appropriate analysis methods in the inner layer. Experiments show that, compared to the state-of-the-art techniques, the proposed framework can improve the real-time schedulability of NP-FP task sets by an average of 15.2% with a maximum improvement of 233.6% (when tasks are highly cache-sensitive) and a minimum of 1.6% (when cache sensitivity is low). For such task sets, we found that clustering similar-period (or mutually compatible) tasks often leads to higher schedulability (on average 7.6%) than clustering by cache sensitivity. In our evaluation, the framework also achieves good results for preemptive and dynamic-priority scheduling policies.

Modern language models are increasingly asked to handle several tasks within a single prompt. Doing so requires solving each task correctly while integrating the resulting answers into a coherent response. In this paper, we identify a fundamental limitation in this process, where models make substantially more errors when tasks are composed, even when they can solve every constituent task reliably in isolation. This degradation cannot be fully explained by the accumulation of independent errors. Across both open-weight models and the frontier model Claude Opus 5, our findings instead point to an implicit thinking budget underlying this effect. In particular, under composition, models use substantially fewer tokens per task than in isolation, even when the full sequence remains well within the context window. Tasks that require longer solution traces in isolation are consequently more fragile under composition, i.e., models make more errors on prompts containing these tasks. In isolation, non-fragile tasks receive more reasoning than they need and waste compute. However, by grouping tasks according to their fragility, the implicit budgeting can be manipulated to reduce token usage by 43\% across a range of math and linguistic tasks while also preserving accuracy.

This paper introduces SCHEDBench, a natural-language benchmark for evaluating combinatorial scheduling constraint faithfulness under surface-form variation. Grounded in canonical scheduling instances and solver-derived feasibility and optimality, SCHEDBench assesses whether large language models (LLMs) generate schedules with the same constraint-feasible behavior across varied natural-language (NL) surface forms. SCHEDBench spans 1,132 instances across job-shop scheduling problems (JSP), single and multi-mode resource-constrained project scheduling problems (RCPSP), nurse rostering/scheduling, and curriculum timetabling problems of varying difficulty. Instances are templated into natural language problems using domain-specific templates, themed entities, lexical-syntactic template rephrasing, and constraint-level surface-form variation, with reference solutions verified for feasibility and objective optimality. Across thirteen frontier and open-weight LLMs, we find that models are not reliably invariant to semantically equivalent renderings of the same scheduling problem. Surface-form variation reduces feasibility and induces above-noise shifts in per-instance hard-constraint violations on matched instances. Among the tested isolated axes, constraint reordering yields the clearest above-noise sensitivity.

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (Principled and Efficient Test-TimeSelf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the self-consistency rate, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to 75% (offline) and 55% (online) relative to uniform allocation. Code is available at https://github.com/ZDCSlab/PETS.

AI agents are increasingly deployed in multi-tenant cloud environments, where they execute diverse tool calls within sandboxed containers, each call with distinct resource demands and rapid fluctuations. We present a systematic characterization of OS-level resource dynamics in sandboxed AI coding agents, analyzing 144 software engineering tasks from the SWE-rebench benchmark across two LLM models. Our measurements reveal that (1) OS-level execution (tool calls, container and agent initialization) accounts for 56-74% of end-to-end task latency; (2) memory, not CPU, is the concurrency bottleneck; (3) memory spikes are tool-call-driven with a up to 15.4x peak-to-average ratio; and (4) resource demands are highly unpredictable across tasks, runs, and models. Comparing these characteristics against serverless, microservice, and batch workloads, we identify three mismatches in existing resource controls: a granularity mismatch (container-level policies vs. tool-call-level dynamics), a responsiveness mismatch (user-space reaction vs. sub-second unpredictable bursts), and an adaptability mismatch (history-based prediction vs. non-deterministic stateful execution). We propose AgentCgroup, an intent-driven eBPF-based resource controller that exploits agents ability to declare resource needs and reconstruct execution strategies, using hierarchical cgroup structures aligned with tool-call boundaries, in-kernel enforcement via sched_ext and memcg_bpf_ops, and runtime-adaptive policies. Preliminary evaluation demonstrates improved multi-tenant isolation and reduced resource waste. AgentCgroup is open-source at https://github.com/eunomia-bpf/agentcgroup

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n points in a metric space (P,d) where each point belongs to one of the ell different demographics (i.e., P = P_1 uplus P_2 uplus cdots uplus P_ell) and a set of ell intervals [alpha_1, beta_1], cdots, [alpha_ell, beta_ell] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ell_p-clustering cost (i.e., (sum_{vin P} d(v,C)^p)^{1/p}) such that for each group iin ell, |Ccap P_i| in [alpha_i, beta_i]. In particular, the fair range ell_p-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range ell_p-clustering for all values of pin [1,infty).

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal O(T) regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an O(T) regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Reinforcement learning with verifiable rewards (RLVR) generates hundreds of thousands of tokens per training step, with rollout generation dominating the computational cost. The overall token budget can be controlled along two main dimensions: (i) deciding which prompts to allocate rollouts to, and (ii) deciding how long each rollout should be. Prior work has generally controlled only one of these dimensions at a time. We show that jointly tuning both decisions under a shared compute budget improves both reasoning quality and wall-clock training time. We instantiate this view as DUal-controlled tokEn allocaTion (DUET), a computationally efficient layer over GRPO that uses a lightweight pre-rollout surrogate of prompt informativeness to set how many rollouts each prompt receives, and a marker-gated abort rule with importance reweighting to set when to stop them. On Qwen3-1.7B trained on MATH, DUET outperforms full-budget GRPO and the other three budget-aware baseline methods. DUET's advantage further generalizes to other benchmarks across math and coding, and is on par with the best baseline on the scientific Q\&A domain, while also achieving a 1.62times wall-clock speedup. More notably, using only 50\% of the token budget, DUET still outperforms all baseline methods at their full budget, achieving an even higher 2.51times speedup over full-budget GRPO. We verify the high performance of DUET on other backbone LLMs, including Qwen3-4B and Llama-3.2-3B-Instruct. Notably, the gap between DUET and the strongest baseline widens as the budget tightens, contrary to the usual pattern in which efficient methods trade off quality as compute decreases. More broadly, these results suggest that DUET budget-aware control strategies are valuable not only for accelerating training, but also for improving the quality of the learning signal.

Scheduling precedence-constrained tasks under shared renewable resources is central to modern computing platforms. The Resource Investment Problem (RIP) models this setting by minimizing the cost of provisioned renewable resources under precedence and timing constraints. Exact mixed-integer programming and constraint programming become impractically slow on large instances, and dynamic updates require schedule revisions under tight latency budgets. We present iScheduler, a reinforcement-learning-driven iterative scheduling framework that formulates RIP solving as a Markov decision process over decomposed subproblems and constructs schedules through sequential process selection. The framework accelerates optimization and supports reconfiguration by reusing unchanged process schedules and rescheduling only affected processes. We also release L-RIPLIB, an industrial-scale benchmark derived from cloud-platform workloads with 1,000 instances of 2,500-10,000 tasks. Experiments show that iScheduler attains competitive resource costs while reducing time to feasibility by up to 43times against strong commercial baselines.

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations. Initially before creating a route, each vehicle needs a group of delivery points that are not exceeding their maximum capacity. Drivers tend to deliver only to certain areas. Cluster-based is one of the approaches to give a basis for generating tighter routes. In this paper we propose new algorithms for producing such clusters/groups that do not exceed vehicles maximum capacity. Our basic assumptions are each vehicle originates from a depot, delivers the items to the customers and returns to the depot, also the vehicles are homogeneous. This methods are able to compact sub-areas in each cluster. Computational results demonstrate the effectiveness of our new procedures, which are able to assist users to plan service territories and vehicle routes more efficiently.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising. In many of these application domains the learner may be constrained by one or more supply (or budget) limits, in addition to the customary limitation on the time horizon. The literature lacks a general model encompassing these sorts of problems. We introduce such a model, called "bandits with knapsacks", that combines aspects of stochastic integer programming with online learning. A distinctive feature of our problem, in comparison to the existing regret-minimization literature, is that the optimal policy for a given latent distribution may significantly outperform the policy that plays the optimal fixed arm. Consequently, achieving sublinear regret in the bandits-with-knapsacks problem is significantly more challenging than in conventional bandit problems. We present two algorithms whose reward is close to the information-theoretic optimum: one is based on a novel "balanced exploration" paradigm, while the other is a primal-dual algorithm that uses multiplicative updates. Further, we prove that the regret achieved by both algorithms is optimal up to polylogarithmic factors. We illustrate the generality of the problem by presenting applications in a number of different domains including electronic commerce, routing, and scheduling. As one example of a concrete application, we consider the problem of dynamic posted pricing with limited supply and obtain the first algorithm whose regret, with respect to the optimal dynamic policy, is sublinear in the supply.

Modern cloud data warehouses store data in micro-partitions and rely on metadata (e.g., zonemaps) for efficient data pruning during query processing. Maintaining data clustering in a large-scale table is crucial for effective data pruning. Existing automatic clustering approaches lack the flexibility required in dynamic cloud environments with continuous data ingestion and evolving workloads. This paper advocates a clean separation between reclustering policy and clustering-key selection. We introduce the concept of boundary micro-partitions that sit on the boundary of query ranges. We then present WAIR, a workload-aware algorithm to identify and recluster only boundary micro-partitions most critical for pruning efficiency. WAIR achieves near-optimal (with respect to fully sorted table layouts) query performance but incurs significantly lower reclustering cost with a theoretical upper bound. We further implement the algorithm into a prototype reclustering service and evaluate on standard benchmarks (TPC-H, DSB) and a real-world workload. Results show that WAIR improves query performance and reduces the overall cost compared to existing solutions.

Mixture-of-Experts (MoE) language models scale model ability with sparsely activated experts, making this architecture a standard recipe for modern large models. However, sparse activation does not remove the deployment burden of storing and serving all experts, and the available deployment budget can vary substantially across devices, users, and workloads. Existing MoE compression methods are still largely fixed-budget, typically optimizing one compressed endpoint at each chosen target budget. We study a different setting: converting a large pretrained MoE LLM into a nested family of deployable subnetworks across budgets. Our method first ranks expert FFN channels by their importance, then lets each expert learn a discrete action to prune its channels. By gradually increasing cost pressure, a single action-training run exports a series of action masks from high to low budgets, each of which identifies a reliable smaller subnetwork nested in the ranked base model. Moreover, we use a single recovery fine-tune at a mid pruning budget (40%) to recover degraded model quality and transfer the recovered model to other unseen budgets. Overall, our framework surpasses recent MoE compression baselines. Specifically, on Qwen2-57B-A14B, our method retains ~99.8% of base performance while pruning 50% of routed expert parameters even without fine-tuning. For deployment, our pruned subnetworks deliver real memory reduction and throughput gains, and further support realtime online budget switching with kernel-level co-design.

The proliferation of Large Language Models (LLMs) has established LLM routing as a standard service delivery mechanism, where users select models based on cost, Quality of Service (QoS), among other things. However, optimal pricing in LLM routing platforms requires precise modeling for dynamic service markets, and solving this problem in real time at scale is computationally intractable. In this paper, we propose \PriLLM, a novel practical and scalable solution for real-time dynamic pricing in competitive LLM routing. \PriLLM models the service market as a Stackelberg game, where providers set prices and users select services based on multiple criteria. To capture real-world market dynamics, we incorporate both objective factors (\eg~cost, QoS) and subjective user preferences into the model. For scalability, we employ a deep aggregation network to learn provider abstraction that preserve user-side equilibrium behavior across pricing strategies. Moreover, \PriLLM offers interpretability by explaining its pricing decisions. Empirical evaluation on real-world data shows that \PriLLM achieves over 95\% of the optimal profit while only requiring less than 5\% of the optimal solution's computation time.

Effective scheduling under tight resource, timing, and operational constraints underpins large-scale planning across sectors such as capital projects, manufacturing, logistics, and IT fleet transitions. However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact, implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

Effective multi-user delay-constrained scheduling is crucial in various real-world applications, including embodied AI, instant messaging, live streaming, and data center management, where efficient resource allocation is required among users with diverse delay sensitivities. In these scenarios, schedulers must make real-time decisions to satisfy both delay and resource constraints without prior knowledge of system dynamics, which are often time-varying and challenging to estimate. {Current learning-based methods typically require online interactions with actual systems during the training stage. Therefore, these approaches are often difficult or impractical, as they can significantly degrade system performance and incur substantial service costs.} To address these challenges, we propose a novel offline reinforcement learning-based algorithm, named Scheduling By Offline Learning with Critic Guidance and Diffusion Model (SOCD), to learn efficient scheduling policies purely from pre-collected offline data. SOCD innovatively employs a diffusion policy, complemented by a sampling-free critic network for policy guidance. By integrating the Lagrangian multiplier optimization into the offline reinforcement learning, SOCD efficiently trains high-quality constraint-aware policies exclusively from available datasets, eliminating the need for online interactions with the system. Experimental results demonstrate that SOCD is resilient to various system dynamics, including partially observable and large-scale environments, and delivers superior performance compared to existing methods.

We consider the linear contextual bandit problem with resource consumption, in addition to reward generation. In each round, the outcome of pulling an arm is a reward as well as a vector of resource consumptions. The expected values of these outcomes depend linearly on the context of that arm. The budget/capacity constraints require that the total consumption doesn't exceed the budget for each resource. The objective is once again to maximize the total reward. This problem turns out to be a common generalization of classic linear contextual bandits (linContextual), bandits with knapsacks (BwK), and the online stochastic packing problem (OSPP). We present algorithms with near-optimal regret bounds for this problem. Our bounds compare favorably to results on the unstructured version of the problem where the relation between the contexts and the outcomes could be arbitrary, but the algorithm only competes against a fixed set of policies accessible through an optimization oracle. We combine techniques from the work on linContextual, BwK, and OSPP in a nontrivial manner while also tackling new difficulties that are not present in any of these special cases.

Layer fusion techniques are critical to improving the inference efficiency of deep neural networks (DNN) for deployment. Fusion aims to lower inference costs by reducing data transactions between an accelerator's on-chip buffer and DRAM. This is accomplished by grouped execution of multiple operations like convolution and activations together into single execution units - fusion groups. However, on-chip buffer capacity limits fusion group size and optimizing fusion on whole DNNs requires partitioning into multiple fusion groups. Finding the optimal groups is a complex problem where the presence of invalid solutions hampers traditional search algorithms and demands robust approaches. In this paper we incorporate Explainable AI, specifically Graph Explanation Techniques (GET), into layer fusion. Given an invalid fusion group, we identify the operations most responsible for group invalidity, then use this knowledge to recursively split the original fusion group via a greedy tree-based algorithm to minimize DRAM access. We pair our scheme with common algorithms and optimize DNNs on two types of layer fusion: Line-Buffer Depth First (LBDF) and Branch Requirement Reduction (BRR). Experiments demonstrate the efficacy of our scheme on several popular and classical convolutional neural networks like ResNets and MobileNets. Our scheme achieves over 20% DRAM Access reduction on EfficientNet-B3.

Text clustering aims to automatically partition a collection of documents into coherent groups based on their linguistic features. In the literature, this task is formulated either as metric clustering over pre-trained text embeddings or as graph clustering based on pairwise similarities derived from an oracle, e.g., a large machine learning model. Recent advances in large language models (LLMs) have significantly improved this field by providing high-quality contextualized embeddings and accurate semantic similarity estimates. However, leveraging LLMs at scale introduces substantial computational and financial costs due to the large number of required API queries or inference calls. To address this issue, we propose Cequel, a cost-effective framework that achieves accurate text clustering under a limited budget of LLM queries. At its core, Cequel constructs must-link and cannot-link constraints by selectively querying LLMs on informative text pairs or triplets, identified via our proposed algorithms, EdgeLLM and TriangleLLM. These constraints are then utilized in a weighted constrained clustering algorithm to form high-quality clusters. Specifically, EdgeLLM and TriangleLLM employ carefully designed greedy selection strategies and prompting techniques to identify and extract informative constraints efficiently. Experiments on multiple benchmark datasets demonstrate that Cequel consistently outperforms existing methods in unsupervised text clustering under the same query budget.

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent β; communication is captured by a message-length fidelity curve γ(m); dependence is captured by an effective shared-error correlation ρ; and a context window W imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep b-ary trees with correlated inputs and lossy communication: a single scalar α_ρ (combining γ(m), ρ, and fan-in b) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent s and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when s>β, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

As LLMs proliferate with diverse capabilities and costs, LLM routing has emerged by learning to predict each LLM's quality and cost for a given query, then selecting the one with high quality and low cost. However, existing routers implicitly assume a single fixed quality and cost per LLM for each query, ignoring that the same LLM's quality varies with its output length. This causes routers to exclude powerful LLMs when their estimated cost exceeds the budget, missing the opportunity that these LLMs could still deliver high quality at reduced cost with shorter outputs. To address this, we introduce R2-Router, which treats output length budget as a controllable variable and jointly selects the best LLM and length budget, enforcing the budget via length-constrained instructions. This enables R2-Router to discover that a powerful LLM with constrained output can outperform a weaker LLM at comparable cost-efficient configurations invisible to prior methods. Together with the router framework, we construct R2-Bench, the first routing dataset capturing LLM behavior across diverse output length budgets. Experiments show that R2-Router achieves state-of-the-art performance at 4-5x lower cost compared with existing routers. This work opens a new direction: routing as reasoning, where routers evolve from reactive selectors to deliberate reasoners that explore which LLM to use and at what cost budget.

Designing effective agentic systems requires the seamless composition and integration of agents, tools, and models within dynamic and uncertain environments. Most existing methods rely on static, semantic retrieval approaches for tool or agent discovery. However, effective reuse and composition of existing components remain challenging due to incomplete capability descriptions and the limitations of retrieval methods. Component selection suffers because the decisions are not based on capability, cost, and real-time utility. To address these challenges, we introduce a structured, automated framework for agentic system composition that is inspired by the knapsack problem. Our framework enables a composer agent to systematically identify, select, and assemble an optimal set of agentic components by jointly considering performance, budget constraints, and compatibility. By dynamically testing candidate components and modeling their utility in real-time, our approach streamlines the assembly of agentic systems and facilitates scalable reuse of resources. Empirical evaluation with Claude 3.5 Sonnet across five benchmarking datasets shows that our online-knapsack-based composer consistently lies on the Pareto frontier, achieving higher success rates at significantly lower component costs compared to our baselines. In the single-agent setup, the online knapsack composer shows a success rate improvement of up to 31.6% in comparison to the retrieval baselines. In multi-agent systems, the online knapsack composer increases success rate from 37% to 87% when agents are selected from an agent inventory of 100+ agents. The substantial performance gap confirms the robust adaptability of our method across diverse domains and budget constraints.

Instruction Tuning involves finetuning a language model on a collection of instruction-formatted datasets in order to enhance the generalizability of the model to unseen tasks. Studies have shown the importance of balancing different task proportions during finetuning, but finding the right balance remains challenging. Unfortunately, there's currently no systematic method beyond manual tuning or relying on practitioners' intuition. In this paper, we introduce SMART (Submodular data Mixture strAtegy for instRuction Tuning) - a novel data mixture strategy which makes use of a submodular function to assign importance scores to tasks which are then used to determine the mixture weights. Given a fine-tuning budget, SMART redistributes the budget among tasks and selects non-redundant samples from each task. Experimental results demonstrate that SMART significantly outperforms traditional methods such as examples proportional mixing and equal mixing. Furthermore, SMART facilitates the creation of data mixtures based on a few representative subsets of tasks alone and through task pruning analysis, we reveal that in a limited budget setting, allocating budget among a subset of representative tasks yields superior performance compared to distributing the budget among all tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/SMART.

Large Language Models (LLMs) show potential for complex reasoning, yet their capacity for emergent coordination in Multi-Agent Systems (MAS) when operating under strict constraints-such as limited local perception and communication, characteristic of natural swarms-remains largely unexplored, particularly concerning the nuances of swarm intelligence. Existing benchmarks often do not fully capture the unique challenges of decentralized coordination that arise when agents operate with incomplete spatio-temporal information. To bridge this gap, we introduce SwarmBench, a novel benchmark designed to systematically evaluate the swarm intelligence capabilities of LLMs acting as decentralized agents. SwarmBench features five foundational MAS coordination tasks within a configurable 2D grid environment, forcing agents to rely primarily on local sensory input (k x k view) and local communication. We propose metrics for coordination effectiveness and analyze emergent group dynamics. Evaluating several leading LLMs in a zero-shot setting, we find significant performance variations across tasks, highlighting the difficulties posed by local information constraints. While some coordination emerges, results indicate limitations in robust planning and strategy formation under uncertainty in these decentralized scenarios. Assessing LLMs under swarm-like conditions is crucial for realizing their potential in future decentralized systems. We release SwarmBench as an open, extensible toolkit-built upon a customizable and scalable physical system with defined mechanical properties. It provides environments, prompts, evaluation scripts, and the comprehensive experimental datasets generated, aiming to foster reproducible research into LLM-based MAS coordination and the theoretical underpinnings of Embodied MAS. Our code repository is available at https://github.com/x66ccff/swarmbench.

Sequential LLM agents fail on long-horizon planning with hard constraints like budgets and diversity requirements. As planning progresses and context grows, these agents drift from global constraints. We propose HiMAP-Travel, a hierarchical multi-agent framework that splits planning into strategic coordination and parallel day-level execution. A Coordinator allocates resources across days, while Day Executors plan independently in parallel. Three key mechanisms enable this: a transactional monitor enforcing budget and uniqueness constraints across parallel agents, a bargaining protocol allowing agents to reject infeasible sub-goals and trigger re-planning, and a single policy trained with GRPO that powers all agents through role conditioning. On TravelPlanner, HiMAP-Travel with Qwen3-8B achieves 52.78% validation and 52.65% test Final Pass Rate (FPR). In a controlled comparison with identical model, training, and tools, it outperforms the sequential DeepTravel baseline by +8.67~pp. It also surpasses ATLAS by +17.65~pp and MTP by +10.0~pp. On FlexTravelBench multi-turn scenarios, it achieves 44.34% (2-turn) and 37.42% (3-turn) FPR while reducing latency 2.5x through parallelization.

Tree-search decoding is an effective form of test-time scaling for large language models (LLMs), but real-world deployment imposes a fixed per-query token budget that varies across settings. Existing tree-search policies are largely budget-agnostic, treating the budget as a termination condition, which can lead to late-stage over-branching or premature termination. We propose {Budget-Guided MCTS} (BG-MCTS), a tree-search decoding algorithm that aligns its search policy with the remaining token budget: it starts with broad exploration, then prioritizes refinement and answer completion as the budget depletes while reducing late-stage branching from shallow nodes. BG-MCTS consistently outperforms budget-agnostic tree-search baselines across different budgets on MATH500 and AIME24/25 with open-weight LLMs.

We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than explicitly simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models agents' computational constraints explicitly, via a latent variable (inferred jointly with a model of agents' goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks -- inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games -- we show that L-IBMs match or outperform Boltzmann models of decision-making under uncertainty. Inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty.

Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by k-means), limiting trade-off control, interpretability, and scalability. We introduce DFNMF, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter lambda tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.

The problem of fair multi-agent coordination in decentralized settings is one of the most pressing challenges for building efficient collaborative systems. Resource allocation is based on optimized collective arrangements accounting for agents' needs. Such coordination should not only be computationally efficient but also account for fairness, i.e., equitable redistribution of costs incurred by all agents. Recent literature has proposed several algorithms that efficiently determine optimal plan combinations balancing system-wide efficiency and individual discomfort of agents in a centralized setting. However, these works do not address equitable resource optimization in fully decentralized scenarios, specifically, the optimized redistribution of discomfort among coordinating agents so that none experiences a discomfort level that could lead to loss of incentive or polarization that can disrupt planned operations. In this work, we study the problem of optimizing three objectives: (i) system-wide efficiency, (ii) individuals' comfort and (iii) fairness (i.e., balancing of incurred discomfort costs) in decentralized multi-agent coordination. We design a novel model to optimize those three orthogonal objectives, without any substantial increase in communication and computational overhead. Through experiments on two real-world datasets, we validate the model and demonstrate that it can achieve fairer optimization outcomes, while satisfying agents' preferences and system goals.

Large Language Models (LLMs) have revolutionized natural language processing, but their varying capabilities and costs pose challenges in practical applications. LLM routing addresses this by dynamically selecting the most suitable LLM for each query/task. Previous approaches treat this as a supervised learning problem, assuming complete knowledge of optimal query-LLM pairings. However, real-world scenarios lack such comprehensive mappings and face evolving user queries. We thus propose to study LLM routing as a contextual bandit problem, enabling adaptive decision-making using bandit feedback without requiring exhaustive inference across all LLMs for all queries (in contrast to supervised routing). To address this problem, we develop a shared embedding space for queries and LLMs, where query and LLM embeddings are aligned to reflect their affinity. This space is initially learned from offline human preference data and refined through online bandit feedback. We instantiate this idea through Preference-prior Informed Linucb fOr adaptive rouTing (PILOT), a novel extension of LinUCB. To handle diverse user budgets for model routing, we introduce an online cost policy modeled as a multi-choice knapsack problem, ensuring resource-efficient routing.

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated exceptional capabilities in solving complex tasks, yet their effectiveness depends heavily on the underlying communication topology that coordinates agent interactions. Within these systems, successful problem-solving often necessitates task-specific group structures to divide and conquer subtasks. However, most existing approaches generate communication topologies in a node-centric manner, leaving group structures to emerge implicitly from local connectivity decisions rather than modeling them explicitly, often leading to suboptimal coordination and unnecessary communication overhead. To address this limitation, we propose GoAgent (Group-of-Agents), a communication topology generation method that explicitly treats collaborative groups as the atomic units of MAS construction. Specifically, GoAgent first enumerates task-relevant candidate groups through an LLM and then autoregressively selects and connects these groups as atomic units to construct the final communication graph, jointly capturing intra-group cohesion and inter-group coordination. To mitigate communication redundancy and noise propagation inherent in expanding topologies, we further introduce a conditional information bottleneck (CIB) objective that compresses inter-group communication, preserving task-relevant signals while filtering out redundant historical noise. Extensive experiments on six benchmarks demonstrate the state-of-the-art performance of GoAgent with 93.84% average accuracy while reducing token consumption by about 17%.

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

Large Language Models (LLMs) have demonstrated remarkable generation capabilities but often struggle to access up-to-date information, which can lead to hallucinations. Retrieval-Augmented Generation (RAG) addresses this issue by incorporating knowledge from external databases, enabling more accurate and relevant responses. Due to the context window constraints of LLMs, it is impractical to input the entire external database context directly into the model. Instead, only the most relevant information, referred to as chunks, is selectively retrieved. However, current RAG research faces three key challenges. First, existing solutions often select each chunk independently, overlooking potential correlations among them. Second, in practice the utility of chunks is non-monotonic, meaning that adding more chunks can decrease overall utility. Traditional methods emphasize maximizing the number of included chunks, which can inadvertently compromise performance. Third, each type of user query possesses unique characteristics that require tailored handling, an aspect that current approaches do not fully consider. To overcome these challenges, we propose a cost constrained retrieval optimization system CORAG for retrieval-augmented generation. We employ a Monte Carlo Tree Search (MCTS) based policy framework to find optimal chunk combinations sequentially, allowing for a comprehensive consideration of correlations among chunks. Additionally, rather than viewing budget exhaustion as a termination condition, we integrate budget constraints into the optimization of chunk combinations, effectively addressing the non-monotonicity of chunk utility.

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous O(n^{5/6}polylog(n)) fair approximation for cost to a near polylogarithmic O(n^delta polylog(n)) fair approximation for any constant deltain(0,1). This result establishes a cost-fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

This paper presents a novel approach, named the Group Marching Tree (GMT*) algorithm, to planning on GPUs at rates amenable to application within control loops, allowing planning in real-world settings via repeated computation of near-optimal plans. GMT*, like the Fast Marching Tree (FMT) algorithm, explores the state space with a "lazy" dynamic programming recursion on a set of samples to grow a tree of near-optimal paths. GMT*, however, alters the approach of FMT with approximate dynamic programming by expanding, in parallel, the group of all active samples with cost below an increasing threshold, rather than only the minimum cost sample. This group approximation enables low-level parallelism over the sample set and removes the need for sequential data structures, while the "lazy" collision checking limits thread divergence---all contributing to a very efficient GPU implementation. While this approach incurs some suboptimality, we prove that GMT* remains asymptotically optimal up to a constant multiplicative factor. We show solutions for complex planning problems under differential constraints can be found in ~10 ms on a desktop GPU and ~30 ms on an embedded GPU, representing a significant speed up over the state of the art, with only small losses in performance. Finally, we present a scenario demonstrating the efficacy of planning within the control loop (~100 Hz) towards operating in dynamic, uncertain settings.

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.

The primary way of building AI applications is shifting from training specialist models to prompting generalist models. A common practice for prompting generalist models, often referred to as in-context learning, is to append a few examples (demonstrations) to the prompt to help the model better understand the task. While effective, in-context learning can be inefficient because it makes the input prompt much longer, consuming valuable space in the context window and leading to larger computational costs. In this paper, we propose DynaICL, a recipe for efficient prompting with black-box generalist models that dynamically allocate in-context examples according to the input complexity and the computational budget. To achieve this, we train a meta controller that predicts the number of in-context examples suitable for the generalist model to make a good prediction based on the performance-efficiency trade-off for a specific input. We then dynamically allocate the number of demonstrations for an input according to predictions from the meta controller and the given computation budget. Experimental results show that dynamic example allocation helps achieve a better performance-efficiency trade-off in two practical settings where computational resources or the required performance is constrained. Specifically, DynaICL saves up to 46% token budget compared to the common practice that allocates the same number of in-context examples to each input. We also find that a meta controller trained on a certain backbone model and tasks can successfully generalize to unseen models and tasks.

Test-time scaling improves LLM reasoning by generating and aggregating multiple candidate answers, yet many pipelines use fixed per-query budgets that spend the same compute on easy and difficult prompts. These fixed budgets are also difficult to inspect because they do not explain why a given prompt receives a particular number of samples. We propose adaptive} test-time scaling with a lightweight fuzzy controller that maps interpretable signals, including estimated prompt complexity and model confidence, to a per-query sampling budget. The controller assigns fewer samples to easier or more confident prompts and more samples to harder or less certain prompts, making inference-time compute inspectable rather than fixed or opaque. We evaluate under a fair-alignment protocol with matched decoding settings and controlled answer selection, and compare against best-of-N, compute-aware scaling, and self-certainty-based baselines on question-answering and mathematical reasoning tasks. Across models and datasets, adaptive fuzzy control improves over several standard baselines and remains close to a selector-matched full-budget control while reducing the average number of samples. These findings suggest that interpretable adaptive sampling is a practical direction for more efficient test-time reasoning in large language models.

Language Reasoning Models (LRMs) achieve strong performance by scaling test-time computation but often suffer from ``overthinking'', producing excessively long reasoning traces that increase latency and memory usage. Existing LRMs typically enforce conciseness with uniform length penalties, which over-compress crucial early deduction steps at the sequence level and indiscriminately penalize all queries at the group level. To solve these limitations, we propose \model, a dual-level framework for prefix-protected and difficulty-aware compression under hierarchical supervision. At the sequence level, prefix-protected optimization employs decaying mixed rollouts to maintain valid reasoning paths while promoting conciseness. At the group level, difficulty-aware penalty dynamically scales length constraints based on query complexity, maintaining exploration for harder questions while curbing redundancy on easier ones. Extensive experiments on DeepSeek-R1-Distill-Qwen (1.5B/7B) demonstrate that \model achieves a substantial reduction in token usage (up to 55.7\%) while simultaneously improving accuracy (up to 4.1\%) on math benchmarks, with generalization ability to code, science, and general domains.

Large language models (LLMs) deliver superior performance but require substantial computational resources and operate with relatively low efficiency, while smaller models can efficiently handle simpler tasks with fewer resources. LLM routing is a crucial paradigm that dynamically selects the most suitable large language models from a pool of candidates to process diverse inputs, ensuring optimal resource utilization while maintaining response quality. Existing routing frameworks typically model this as a locally optimal decision-making problem, selecting the presumed best-fit LLM for each query individually, which overlooks global budget constraints, resulting in ineffective resource allocation. To tackle this problem, we introduce OmniRouter, a fundamentally controllable routing framework for multi-LLM serving. Instead of making per-query greedy choices, OmniRouter models the routing task as a constrained optimization problem, assigning models that minimize total cost while ensuring the required performance level. Specifically, a hybrid retrieval-augmented predictor is designed to predict the capabilities and costs of LLMs. After obtaining the predicted cost and performance, we utilize a constrained optimizer for cost-optimal assignments that employs Lagrangian dual decomposition with adaptive multipliers. It iteratively converges toward the globally optimal query-model allocation, dynamically balancing latency minimization against quality thresholds while adhering to heterogeneous capacity constraints. Experiments show that OmniRouter achieves up to 6.30% improvement in response accuracy while simultaneously reducing computational costs by at least 10.15% compared to competitive router baselines. The code and the dataset are available at https://github.com/dongyuanjushi/OmniRouter.

Multi-attribute user records are inherently heterogeneous, often combining continuous, categorical, and binary attributes, and they frequently exhibit strong cross-attribute dependencies. Designing high-utility metric differential privacy (mDP) mechanisms for such records is challenging. Simple predefined mechanisms, such as distance-based noise, may be poorly aligned with task-specific utility loss, whereas fully optimization-based mechanisms can be computationally prohibitive for multi-attribute records. We propose Dependency-aware Heterogeneous Data Perturbation (DepHDP)}, a framework for multi-attribute mDP that combines dependency-aware attribute grouping with heterogeneous perturbation design. Rather than applying a one-size-fits-all mechanism, DepHDP selects an appropriate perturbation strategy for each attribute or attribute group, choosing between efficient predefined mechanisms, such as Laplace or Exponential mechanisms, and optimization-based designs. This selection is guided by both domain size and a predefined-noise adequacy criterion, which quantifies whether task-induced utility loss can be well explained by perturbation magnitude. To support scalable end-to-end optimization, DepHDP estimates group-level utility loss through sampling and lightweight surrogate modeling, and jointly optimizes privacy-budget allocation and group-wise mechanism design under a global ell_p-metric mDP constraint. Across three case studies, DepHDP improves privacy--utility trade-offs over uniform baselines at lower computational cost than full-record OPT on evaluated domains.

Planning for real-world problems by language models often involves both world and user constraints, which may not be fully specified upfront and are progressively disclosed through interaction. However, existing benchmarks still underexplore adaptive planning under such progressively revealed dual constraints. To address this gap, we introduce AdaPlanBench, a dynamic interactive benchmark for evaluating whether Large Language Model (LLM) agents can adaptively plan and re-plan under progressively revealed world and user constraints. AdaPlanBench is built on 307 household tasks, with a scalable constraint construction pipeline that augments each task with dual constraints. At runtime, agents interact with the environment in a multi-turn protocol where hidden constraints are revealed only when the agent proposes a plan that violates them, requiring iterative plan revision under accumulating feedback. This makes planning challenging, as agents must infer and track constraints from feedback while re-planning effectively. Experiments on ten leading LLMs show that adaptive planning under dual constraints remains challenging, with the best model reaching only 67.75% accuracy. We further observe that performance degrades as more constraints accumulate, with user constraints posing a particularly large challenge and failures often stemming from weaker physical grounding and reduced effectiveness. These results establish AdaPlanBench as a testbed for dual-constrained interactive planning and highlight the challenge of reliable adaptation to dynamically revealed constraints in LLM agents.

This paper formalizes threshold-based selection as an evaluation-gating architecture in which each incumbent is tested before variation and a replacement is generated and evaluated only when contextual pressure exceeds intrinsic strength. The mechanism is instantiated as Leaf Abscission Optimization (LAO), using rank-based strength, a phenological seasonal signal, diversity modulation, environmental pressure, and a base regrowth kernel. A blocked two-to-the-fourth-power factorial analysis at dimension 10 on the CEC 2017 suite reduces the original multi-layer design to a parsimonious core: drift is harmful, while the other three auxiliary layers show no robust independent evidence of benefit. The resulting LAO-Core attains the third-best mean Friedman rank among nine optimizers at dimensions 10, 30, and 50 under the equal evaluation budget. A four-budget sweep shows budget-dependent relative performance, with adaptive differential-evolution baselines gaining relative advantage at larger budgets; the nine-cell dimension-budget analysis establishes neither an evaluation-budget-per-dimension-only law nor a statistically significant dimension-budget interaction. A paired intervention shows that diversity modulation changes late-run replacement behaviour without a detectable effect on final error at the tested budget. The evidence supports LAO as a parsimonious evaluation-gating mechanism with regime-qualified competitiveness, rather than as a generally superior optimizer.

Large language models (LLMs) with chain-of-thought reasoning have demonstrated remarkable problem-solving capabilities, but controlling their computational effort remains a significant challenge for practical deployment. Recent proprietary systems like OpenAI's gpt-oss series have introduced discrete operational modes for intuitive reasoning control, but the open-source community has largely failed to achieve such capabilities. In this paper, we introduce ThinkDial, the first open-recipe end-to-end framework that successfully implements gpt-oss-style controllable reasoning through discrete operational modes. Our system enables seamless switching between three distinct reasoning regimes: High mode (full reasoning capability), Medium mode (50 percent token reduction with <10 percent performance degradation), and Low mode (75 percent token reduction with <15 percent performance degradation). We achieve this through an end-to-end training paradigm that integrates budget-mode control throughout the entire pipeline: budget-mode supervised fine-tuning that embeds controllable reasoning capabilities directly into the learning process, and two-phase budget-aware reinforcement learning with adaptive reward shaping. Extensive experiments demonstrate that ThinkDial achieves target compression-performance trade-offs with clear response length reductions while maintaining performance thresholds. The framework also exhibits strong generalization capabilities on out-of-distribution tasks.

With the development of LLMs as agents, there is a growing interest in connecting multiple agents into multi-agent systems to solve tasks concurrently, focusing on their role in task assignment and coordination. This paper explores how LLMs can effectively allocate computational tasks among multiple agents, considering factors such as cost, efficiency, and performance. In this work, we address key questions, including the effectiveness of LLMs as orchestrators and planners, comparing their effectiveness in task assignment and coordination. Our experiments demonstrate that LLMs can achieve high validity and accuracy in resource allocation tasks. We find that the planner method outperforms the orchestrator method in handling concurrent actions, resulting in improved efficiency and better utilization of agents. Additionally, we show that providing explicit information about worker capabilities enhances the allocation strategies of planners, particularly when dealing with suboptimal workers.

The emergence of Large Language Models (LLMs) like ChatGPT has inspired the development of LLM-based agents capable of addressing complex, real-world tasks. However, these agents often struggle during task execution due to methodological constraints, such as error propagation and limited adaptability. To address this issue, we propose a multi-agent framework based on dynamic Task Decomposition and Agent Generation (TDAG). This framework dynamically decomposes complex tasks into smaller subtasks and assigns each to a specifically generated subagent, thereby enhancing adaptability in diverse and unpredictable real-world tasks. Simultaneously, existing benchmarks often lack the granularity needed to evaluate incremental progress in complex, multi-step tasks. In response, we introduce ItineraryBench in the context of travel planning, featuring interconnected, progressively complex tasks with a fine-grained evaluation system. ItineraryBench is designed to assess agents' abilities in memory, planning, and tool usage across tasks of varying complexity. Our experimental results reveal that TDAG significantly outperforms established baselines, showcasing its superior adaptability and context awareness in complex task scenarios.

Dynamic adaptation has become an essential technique in accelerating distributed machine learning (ML) training. Recent studies have shown that dynamically adjusting model structure (e.g., lottery ticket hypothesis) or hyperparameters (e.g., batch size) can significantly accelerate training without sacrificing accuracy. However, existing ML cluster schedulers are not designed to handle dynamic adaptation. We show that existing schemes fail to provide fairness and degrade system efficiency when the training throughput changes over time under dynamic adaptation. We design Shockwave, a scheduler with future planning that builds on two key ideas. First, Shockwave extends classic market theory from static settings to dynamic settings to co-optimize efficiency and fairness. Second, Shockwave utilizes stochastic dynamic programming to handle dynamic changes. We build a system for Shockwave and validate its performance with both trace-driven simulation and cluster experiments. Results show that for traces of ML jobs with dynamic adaptation, Shockwave improves makespan by 1.3X and fairness by 2X when compared with existing fair scheduling schemes.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

We propose a cluster-based frame selection strategy to mitigate information leakage in video-derived frames datasets. By grouping visually similar frames before splitting into training, validation, and test sets, the method produces more representative, balanced, and reliable dataset partitions.

Recent deep-thinking large language models often reason extensively to improve performance, but such lengthy reasoning is not always desirable, as it incurs excessive inference costs with disproportionate performance gains. Controlling reasoning length without sacrificing performance is therefore important, but remains challenging, especially under tight thinking budgets. We propose budget guidance, a simple yet effective method for steering the reasoning process of LLMs toward a target budget without requiring any LLM fine-tuning. Our approach introduces a lightweight predictor that models a Gamma distribution over the remaining thinking length during next-token generation. This signal is then used to guide generation in a soft, token-level manner, ensuring that the overall reasoning trace adheres to the specified thinking budget. Budget guidance enables natural control of the thinking length, along with significant token efficiency improvements over baseline methods on challenging math benchmarks. For instance, it achieves up to a 26% accuracy gain on the MATH-500 benchmark under tight budgets compared to baseline methods, while maintaining competitive accuracy with only 63% of the thinking tokens used by the full-thinking model. Budget guidance also generalizes to broader task domains and exhibits emergent capabilities, such as estimating question difficulty. The source code is available at: https://github.com/UMass-Embodied-AGI/BudgetGuidance.

Task allocation is a key combinatorial optimization problem, crucial for modern applications such as multi-robot cooperation and resource scheduling. Decision makers must allocate entities to tasks reasonably across different scenarios. However, traditional methods assume static attributes and numbers of tasks and entities, often relying on dynamic programming and heuristic algorithms for solutions. In reality, task allocation resembles Markov decision processes, with dynamically changing task and entity attributes. Thus, algorithms must dynamically allocate tasks based on their states. To address this issue, we propose a two-stage task allocation algorithm based on similarity, utilizing reinforcement learning to learn allocation strategies. The proposed pre-assign strategy allows entities to preselect appropriate tasks, effectively avoiding local optima and thereby better finding the optimal allocation. We also introduce an attention mechanism and a hyperparameter network structure to adapt to the changing number and attributes of entities and tasks, enabling our network structure to generalize to new tasks. Experimental results across multiple environments demonstrate that our algorithm effectively addresses the challenges of dynamic task allocation in practical applications. Compared to heuristic algorithms like genetic algorithms, our reinforcement learning approach better solves dynamic allocation problems and achieves zero-shot generalization to new tasks with good performance. The code is available at https://github.com/yk7333/TaskAllocation.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key approach for enhancing LLM reasoning.However, standard frameworks like Group Relative Policy Optimization (GRPO) typically employ a uniform rollout budget, leading to resource inefficiency. Moreover, existing adaptive methods often rely on instance-level metrics, such as task pass rates, failing to capture the model's dynamic learning state. To address these limitations, we propose CoBA-RL, a reinforcement learning algorithm designed to adaptively allocate rollout budgets based on the model's evolving capability. Specifically, CoBA-RL utilizes a Capability-Oriented Value function to map tasks to their potential training gains and employs a heap-based greedy strategy to efficiently self-calibrate the distribution of computational resources to samples with high training value. Extensive experiments demonstrate that our approach effectively orchestrates the trade-off between exploration and exploitation, delivering consistent generalization improvements across multiple challenging benchmarks. These findings underscore that quantifying sample training value and optimizing budget allocation are pivotal for advancing LLM post-training efficiency.

GUI agents accumulate high-resolution screenshots as the trajectory unfolds, increasing inference latency and memory usage. Training-free visual token pruning can reduce this cost, but cache reuse introduces a fundamental constraint. Once tokens are discarded, the corresponding visual evidence cannot be recovered without re-encoding. Pruning therefore becomes an irreversible admission decision that must remain useful for unknown future targets while preserving coverage of operable regions under tight budgets. To address these challenges, we propose \method{}, a training-free framework for \textbf{Trajectory-robust Admission and Coverage-aware Evidence ordering}. Specifically, we combine a query-independent layout-derived interaction prior with instruction relevance and feature novelty to rank visual evidence according to both potential future utility and diversity. Then, we reserve part of the budget for native visual tokens distributed across the screen, repairing missing spatial coverage without breaking the ordering. Together, these mechanisms produce a nested token order, allowing retained visual evidence to shrink monotonically across budgets while remaining reusable throughout the trajectory. Finally, our monotone KV contraction incrementally contracts retired frames into compact session state, avoiding repeated visual encoding or pruning. Extensive experiments across six GUI benchmarks and diverse models verify the effectiveness of our proposed under tight budgets. The source code will be released.

Long-range tasks require reasoning over long inputs. Existing solutions either need large compute budgets, training data, access to model weights, or use complex, task-specific approaches. We present PRISM, which alleviates these concerns by processing information as a stream of chunks, maintaining a structured in-context memory specified by a typed hierarchy schema. This approach demonstrates superior performance to baselines on diverse tasks while using at least 4x smaller contexts than long-context models. Moreover, PRISM is token-efficient. By producing short outputs and efficiently leveraging key-value (KV) caches, it achieves up to 54% cost reduction when compared to alternative short-context approaches. The method also scales down to tiny information chunks (e.g., 500 tokens) without increasing the number of tokens encoded or sacrificing quality. Furthermore, we show that it is possible to generate schemas to generalize our approach to new tasks with minimal effort.

Agents, language model (LM)-based systems that are capable of reasoning, planning, and acting are becoming the dominant paradigm for real-world AI applications. Despite this widespread adoption, the principles that determine their performance remain underexplored, leaving practitioners to rely on heuristics rather than principled design choices. We address this gap by deriving quantitative scaling principles for agent systems. We evaluate this across four diverse benchmarks: Finance-Agent, BrowseComp-Plus, PlanCraft, and Workbench. Using five canonical architectures (Single, Independent, Centralized, Decentralized, Hybrid) instantiated across three LLM families, we perform a controlled evaluation spanning 180 configurations with standardized tools and token budgets. We derive a predictive model using empirical coordination metrics, including efficiency, overhead, error amplification, and redundancy, that achieves cross-validated R^2=0.513. We identify three dominant effects: (1) a tool-coordination trade-off: under fixed computational budgets, tool-heavy tasks suffer disproportionately from multi-agent overhead. (2) a capability saturation: coordination yields diminishing or negative returns (beta=-0.408, p<0.001) once single-agent baselines exceed ~45%. (3) topology-dependent error amplification: independent agents amplify errors 17.2x through unchecked propagation, while centralized coordination contains this to 4.4x. Centralized coordination improves performance by 80.9% on parallelizable tasks like financial reasoning, while decentralized coordination excels on dynamic web navigation (+9.2% vs. +0.2%). Yet for sequential reasoning tasks, all multi-agent variants degraded performance by 39-70%. The framework predicts the optimal coordination strategy for 87% of held-out configurations, providing a predictive principle of agentic scaling based on measurable task properties.

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

We evaluate language models on their ability to explore interactive environments under a limited interaction budget. We introduce three parametric tasks with controllable exploration difficulty, spanning continuous and discrete environments. Across state-of-the-art models, we find systematic under-exploration and suboptimal solutions, with performance often significantly worse than simple explore--exploit heuristic baselines and scaling weakly as the budget increases. Finally, we study two lightweight interventions: splitting a fixed budget into parallel executions, which surprisingly improves performance despite a no-gain theoretical result for our tasks, and periodically summarizing the interaction history, which preserves key discoveries and further improves exploration.

While agents are increasingly spending more resources, today agent cost is mostly measured only after execution. A Budget-Aware Agent (BAGEN) should treat budget as an active control signal, rather than a passive cost metric. We first systematically define budget estimation as internal budgets (from agent computation) and external budgets (from agent actions). We then formalize budget-awareness as progressive interval estimation: at each step of a plan, an agent should predict an upper and lower bound on remaining budget, and alert when completion is unlikely. Scoring with a rollout-replay protocol, we find consistent failure patterns on four environments and five frontier agents: (1) strong agents do not necessarily have strong budget-awareness, with correlation r=0.35. (2) frontier models are consistently over-optimistic, continue spending on tasks that are unlikely to succeed, instead of alerting the user early. (3) budget-aware signal is actionable and trainable. Early stop saves 28-64% tokens on failed trajectories, and SFT+RL strengthens early stop and alert behavior. (4) precise interval calibration remains challenging, with interval coverage capping at 47% after SFT+RL. Project page: https://ragen-ai.github.io/bagen/

We consider the linear contextual multi-class multi-period packing problem (LMMP) where the goal is to pack items such that the total vector of consumption is below a given budget vector and the total value is as large as possible. We consider the setting where the reward and the consumption vector associated with each action is a class-dependent linear function of the context, and the decision-maker receives bandit feedback. LMMP includes linear contextual bandits with knapsacks and online revenue management as special cases. We establish a new estimator which guarantees a faster convergence rate, and consequently, a lower regret in such problems. We propose a bandit policy that is a closed-form function of said estimated parameters. When the contexts are non-degenerate, the regret of the proposed policy is sublinear in the context dimension, the number of classes, and the time horizon T when the budget grows at least as T. We also resolve an open problem posed by Agrawal & Devanur (2016) and extend the result to a multi-class setting. Our numerical experiments clearly demonstrate that the performance of our policy is superior to other benchmarks in the literature.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

The rapid growth of large language models (LLMs) with diverse capabilities, costs, and domains has created a critical need for intelligent model selection at inference time. While smaller models suffice for routine queries, complex tasks demand more capable models. However, static model deployment does not account for the complexity and domain of incoming queries, leading to suboptimal performance and increased costs. Dynamic routing systems that adaptively select models based on query characteristics have emerged as a solution to this challenge. We provide a systematic analysis of state-of-the-art multi-LLM routing and cascading approaches. In contrast to mixture-of-experts architectures, which route within a single model, we study routing across multiple independently trained LLMs. We cover diverse routing paradigms, including query difficulty, human preferences, clustering, uncertainty quantification, reinforcement learning, multimodality, and cascading. For each paradigm, we analyze representative methods and examine key trade-offs. Beyond taxonomy, we introduce a conceptual framework that characterizes routing systems along three dimensions: when decisions are made, what information is used, and how they are computed. This perspective highlights that practical systems are often compositional, integrating multiple paradigms under operational constraints. Our analysis demonstrates that effective multi-LLM routing requires balancing competing objectives. Choosing the optimal routing strategy depends on deployment and computational constraints. Well-designed routing systems can outperform even the most powerful individual models by strategically leveraging specialized capabilities across models while maximizing efficiency gains. Meanwhile, open challenges remain in developing routing mechanisms that generalize across diverse architectures, modalities, and applications.

Travel planning is a realistic task for evaluating the planning and tool-use abilities of LLM agents. However, existing benchmarks typically assume only a single user, thereby avoiding one of the most challenging aspects of real-world scenarios: an agent's ability to identify and resolve conflicts among multiple users. To address this gap, we introduce GroupTravelBench, the first benchmark for multi-user, multi-turn travel planning. Based on real user profiles, POI data, and ticket price data, we synthesize 650 tasks and divide them into three difficulty levels. Beyond standard abilities in single-user itinerary planning, such as multi-step reasoning and tool use, our benchmark further evaluates three key capabilities required for travel agents: (i) elicitation -- proactively engaging in multi-turn dialogue to gather preferences from each user; (ii) coordination -- resolving conflicts among users through compromise or subgrouping strategies; and (iii) planning -- searching for travel plans that maximize overall group utility while maintaining fairness and feasibility. To simulate real-world conversational itinerary planning while enabling reliable tool use and offline evaluation, we build an interactive sandbox environment with cached real-world tool data. We evaluate a wide range of LLMs and find that even frontier models still show substantial weaknesses in preference coverage and group fairness. GroupTravelBench provides a practical and reproducible benchmark for advancing research on LLM agents for real-world travel planning.

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser's value and also competing advertisers' values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in T second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of Tlog T samples per distribution to achieve the optimal O(T)-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal tilde O(T)-regret, while still being robust to noise in the sampling distributions.