Daily Papers

Cooperative multi-agent reinforcement learning (MARL) is widely used to address large joint observation and action spaces by decomposing a centralized control problem into multiple interacting agents. However, such decomposition often introduces additional challenges, including non-stationarity, unstable training, weak coordination, and limited theoretical guarantees. In this paper, we propose the Consensus Multi-Agent Transformer (CMAT), a centralized framework that bridges cooperative MARL to a hierarchical single-agent reinforcement learning (SARL) formulation. CMAT treats all agents as a unified entity and employs a Transformer encoder to process the large joint observation space. To handle the extensive joint action space, we introduce a hierarchical decision-making mechanism in which a Transformer decoder autoregressively generates a high-level consensus vector, simulating the process by which agents reach agreement on their strategies in latent space. Conditioned on this consensus, all agents generate their actions simultaneously, enabling order-independent joint decision making and avoiding the sensitivity to action-generation order in conventional Multi-Agent Transformers (MAT). This factorization allows the joint policy to be optimized using single-agent PPO while preserving expressive coordination through the latent consensus. To evaluate the proposed method, we conduct experiments on benchmark tasks from StarCraft II, Multi-Agent MuJoCo, and Google Research Football. The results show that CMAT achieves superior performance over recent centralized solutions, sequential MARL methods, and conventional MARL baselines. The code for this paper is available at:https://github.com/RS2002/CMAT .

Most recently developed approaches to cooperative multi-agent reinforcement learning in the centralized training with decentralized execution setting involve estimating a centralized, joint value function. In this paper, we demonstrate that, despite its various theoretical shortcomings, Independent PPO (IPPO), a form of independent learning in which each agent simply estimates its local value function, can perform just as well as or better than state-of-the-art joint learning approaches on popular multi-agent benchmark suite SMAC with little hyperparameter tuning. We also compare IPPO to several variants; the results suggest that IPPO's strong performance may be due to its robustness to some forms of environment non-stationarity.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and guiding optimization run into practical and conceptual difficulty when there are independent, multi-dimensional objectives that need to be pursued simultaneously and cannot be reduced to each other. Ethicists have proved several impossibility theorems that stem from this origin; those results appear to show that there is no way of formally specifying what it means for an outcome to be good for a population without violating strong human ethical intuitions (in such cases, the objective function is a social welfare function). We argue that this is a practical problem for any machine learning system (such as medical decision support systems or autonomous weapons) or rigidly rule-based bureaucracy that will make high stakes decisions about human lives: such systems should not use objective functions in the strict mathematical sense. We explore the alternative of using uncertain objectives, represented for instance as partially ordered preferences, or as probability distributions over total orders. We show that previously known impossibility theorems can be transformed into uncertainty theorems in both of those settings, and prove lower bounds on how much uncertainty is implied by the impossibility results. We close by proposing two conjectures about the relationship between uncertainty in objectives and severe unintended consequences from AI systems.

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in [0,1], we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, CoLSTIM, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a d-dimensional feature vector, we show that CoLSTIM achieves a regret of order tilde O( dT) after T learning rounds. Additionally, we also establish the optimality of CoLSTIM by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

Multimodal AI models are increasingly used in fields like healthcare, finance, and autonomous driving, where information is drawn from multiple sources or modalities such as images, texts, audios, videos. However, effectively managing uncertainty - arising from noise, insufficient evidence, or conflicts between modalities - is crucial for reliable decision-making. Current uncertainty-aware machine learning methods leveraging, for example, evidence averaging, or evidence accumulation underestimate uncertainties in high-conflict scenarios. Moreover, the state-of-the-art evidence averaging strategy is not order invariant and fails to scale to multiple modalities. To address these challenges, we propose a novel multimodal learning method with order-invariant evidence fusion and introduce a conflict-based discounting mechanism that reallocates uncertain mass when unreliable modalities are detected. We provide both theoretical analysis and experimental validation, demonstrating that unlike the previous work, the proposed approach effectively distinguishes between conflicting and non-conflicting samples based on the provided uncertainty estimates, and outperforms the previous models in uncertainty-based conflict detection.

The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a history of observations and actions over time. Recent studies have shown that the sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs). Despite these advancements, existing approaches typically involve oracles or steps that are computationally intractable. On the other hand, the upper confidence bound (UCB) based approaches, which have served successfully as computationally efficient methods in bandits and MDPs, have not been investigated for more general PSRs, due to the difficulty of optimistic bonus design in these more challenging settings. This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. We further characterize the sample complexity bounds for our designed UCB-type algorithms for both online and offline PSRs. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.

As artificial intelligence (AI) systems play an increasingly prominent role in human decision-making, challenges surface in the realm of human-AI interactions. One challenge arises from the suboptimal AI policies due to the inadequate consideration of humans disregarding AI recommendations, as well as the need for AI to provide advice selectively when it is most pertinent. This paper presents a sequential decision-making model that (i) takes into account the human's adherence level (the probability that the human follows/rejects machine advice) and (ii) incorporates a defer option so that the machine can temporarily refrain from making advice. We provide learning algorithms that learn the optimal advice policy and make advice only at critical time stamps. Compared to problem-agnostic reinforcement learning algorithms, our specialized learning algorithms not only enjoy better theoretical convergence properties but also show strong empirical performance.

In this paper, we consider the problem of sleeping bandits with stochastic action sets and adversarial rewards. In this setting, in contrast to most work in bandits, the actions may not be available at all times. For instance, some products might be out of stock in item recommendation. The best existing efficient (i.e., polynomial-time) algorithms for this problem only guarantee an O(T^{2/3}) upper-bound on the regret. Yet, inefficient algorithms based on EXP4 can achieve O(T). In this paper, we provide a new computationally efficient algorithm inspired by EXP3 satisfying a regret of order O(T) when the availabilities of each action i in cA are independent. We then study the most general version of the problem where at each round available sets are generated from some unknown arbitrary distribution (i.e., without the independence assumption) and propose an efficient algorithm with O(2^K T) regret guarantee. Our theoretical results are corroborated with experimental evaluations.

Two-player, constant-sum games are well studied in the literature, but there has been limited progress outside of this setting. We propose Joint Policy-Space Response Oracles (JPSRO), an algorithm for training agents in n-player, general-sum extensive form games, which provably converges to an equilibrium. We further suggest correlated equilibria (CE) as promising meta-solvers, and propose a novel solution concept Maximum Gini Correlated Equilibrium (MGCE), a principled and computationally efficient family of solutions for solving the correlated equilibrium selection problem. We conduct several experiments using CE meta-solvers for JPSRO and demonstrate convergence on n-player, general-sum games.

This paper introduces the concept of {mutual consensus} as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the {OWA-MCC} model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.

Decision-making is a dynamic process requiring perception, memory, and reasoning to make choices and find optimal policies. Traditional approaches to decision-making suffer from sample efficiency and generalization, while large-scale self-supervised pretraining has enabled fast adaptation with fine-tuning or few-shot learning in language and vision. We thus argue to integrate knowledge acquired from generic large-scale self-supervised pretraining into downstream decision-making problems. We propose Pretrain-Then-Adapt pipeline and survey recent work on data collection, pretraining objectives and adaptation strategies for decision-making pretraining and downstream inference. Finally, we identify critical challenges and future directions for developing decision foundation model with the help of generic and flexible self-supervised pretraining.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder's parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

In numerous artificial intelligence applications, the collaborative efforts of multiple intelligent agents are imperative for the successful attainment of target objectives. To enhance coordination among these agents, a distributed communication framework is often employed. However, indiscriminate information sharing among all agents can be resource-intensive, and the adoption of manually pre-defined communication architectures imposes constraints on inter-agent communication, thus limiting the potential for effective collaboration. Moreover, the communication framework often remains static during inference, which may result in sustained high resource consumption, as in most cases, only key decisions necessitate information sharing among agents. In this study, we introduce a novel approach wherein we conceptualize the communication architecture among agents as a learnable graph. We formulate this problem as the task of determining the communication graph while enabling the architecture parameters to update normally, thus necessitating a bi-level optimization process. Utilizing continuous relaxation of the graph representation and incorporating attention units, our proposed approach, CommFormer, efficiently optimizes the communication graph and concurrently refines architectural parameters through gradient descent in an end-to-end manner. Additionally, we introduce a temporal gating mechanism for each agent, enabling dynamic decisions on whether to receive shared information at a given time, based on current observations, thus improving decision-making efficiency. Extensive experiments on a variety of cooperative tasks substantiate the robustness of our model across diverse cooperative scenarios, where agents are able to develop more coordinated and sophisticated strategies regardless of changes in the number of agents.

Independence testing is a fundamental and classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) allow stopping earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. It is well known that classical batch tests are not tailored for streaming data settings: valid inference after data peeking requires correcting for multiple testing but such corrections generally result in low power. Following the principle of testing by betting, we design sequential kernelized independence tests (SKITs) that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g, the Hilbert-Schmidt independence criterion. Our test is valid under non-i.i.d. time-varying settings, for which there exist no batch tests. We demonstrate the power of our approaches on both simulated and real data.

The study of decentralized learning or independent learning in cooperative multi-agent reinforcement learning has a history of decades. Recently empirical studies show that independent PPO (IPPO) can obtain good performance, close to or even better than the methods of centralized training with decentralized execution, in several benchmarks. However, decentralized actor-critic with convergence guarantee is still open. In this paper, we propose decentralized policy optimization (DPO), a decentralized actor-critic algorithm with monotonic improvement and convergence guarantee. We derive a novel decentralized surrogate for policy optimization such that the monotonic improvement of joint policy can be guaranteed by each agent independently optimizing the surrogate. In practice, this decentralized surrogate can be realized by two adaptive coefficients for policy optimization at each agent. Empirically, we compare DPO with IPPO in a variety of cooperative multi-agent tasks, covering discrete and continuous action spaces, and fully and partially observable environments. The results show DPO outperforms IPPO in most tasks, which can be the evidence for our theoretical results.

Executing actions in a correlated manner is a common strategy for human coordination that often leads to better cooperation, which is also potentially beneficial for cooperative multi-agent reinforcement learning (MARL). However, the recent success of MARL relies heavily on the convenient paradigm of purely decentralized execution, where there is no action correlation among agents for scalability considerations. In this work, we introduce a Bayesian network to inaugurate correlations between agents' action selections in their joint policy. Theoretically, we establish a theoretical justification for why action dependencies are beneficial by deriving the multi-agent policy gradient formula under such a Bayesian network joint policy and proving its global convergence to Nash equilibria under tabular softmax policy parameterization in cooperative Markov games. Further, by equipping existing MARL algorithms with a recent method of differentiable directed acyclic graphs (DAGs), we develop practical algorithms to learn the context-aware Bayesian network policies in scenarios with partial observability and various difficulty. We also dynamically decrease the sparsity of the learned DAG throughout the training process, which leads to weakly or even purely independent policies for decentralized execution. Empirical results on a range of MARL benchmarks show the benefits of our approach.

We study the problem of cooperative multi-agent reinforcement learning with a single joint reward signal. This class of learning problems is difficult because of the often large combined action and observation spaces. In the fully centralized and decentralized approaches, we find the problem of spurious rewards and a phenomenon we call the "lazy agent" problem, which arises due to partial observability. We address these problems by training individual agents with a novel value decomposition network architecture, which learns to decompose the team value function into agent-wise value functions. We perform an experimental evaluation across a range of partially-observable multi-agent domains and show that learning such value-decompositions leads to superior results, in particular when combined with weight sharing, role information and information channels.

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update their strategies (actors) using feedback from two distinct critics: a fast critic that intuitively responds to observed payoffs under limited information, and a slow critic that deliberatively approximates the solution to the underlying dynamic programming problem. Crucially, the learning process relies on non-equilibrium adaptation through smoothed best responses to observed payoffs. We establish convergence to (approximate) equilibria in two-agent zero-sum and multi-agent identical-interest stochastic games over an infinite horizon. This provides one of the first payoff-based and fully decentralized learning algorithms with theoretical guarantees in both settings. Empirical results further validate the robustness and effectiveness of the proposed approach across both classes of games.

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this purpose, with recent works also using methods based on Nash equilibria. Unfortunately, Elo is unable to handle intransitive agent interactions, and other techniques are restricted to zero-sum, two-player settings or are limited by the fact that the Nash equilibrium is intractable to compute. Recently, a ranking method called α-Rank, relying on a new graph-based game-theoretic solution concept, was shown to tractably apply to general games. However, evaluations based on Elo or α-Rank typically assume noise-free game outcomes, despite the data often being collected from noisy simulations, making this assumption unrealistic in practice. This paper investigates multiagent evaluation in the incomplete information regime, involving general-sum many-player games with noisy outcomes. We derive sample complexity guarantees required to confidently rank agents in this setting. We propose adaptive algorithms for accurate ranking, provide correctness and sample complexity guarantees, then introduce a means of connecting uncertainties in noisy match outcomes to uncertainties in rankings. We evaluate the performance of these approaches in several domains, including Bernoulli games, a soccer meta-game, and Kuhn poker.

Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding non-stationary data and potentially amplifying disparities. We study online learning of a one-dimensional threshold policy from bandit feedback under demographic parity (DP) and, optionally, service-rate constraints. The learner observes only a scalar score each round and selects a threshold; reward and constraint residuals are revealed only for the chosen threshold. We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals for each candidate threshold. At each round, OFS selects a threshold that appears feasible under confidence bounds and, among those, maximizes optimistic reward; if no threshold appears feasible, OFS selects the threshold minimizing optimistic constraint violation. This design directly targets feasible high-utility thresholds and is particularly effective for low-dimensional, interpretable policy classes where discretization is natural. We evaluate OFS on (i) a synthetic closed-loop benchmark with stable contraction dynamics and (ii) two semi-synthetic closed-loop benchmarks grounded in German Credit and COMPAS, constructed by training a score model and feeding group-dependent acceptance decisions back into population composition. Across all environments, OFS achieves higher reward with smaller cumulative constraint violation than unconstrained and primal-dual bandit baselines, and is near-oracle relative to the best feasible fixed threshold under the same sweep procedure. Experiments are reproducible and organized with double-blind-friendly relative outputs.

The progress of AI is bottlenecked by the quality of evaluation, and powerful LLM-as-a-Judge models have proved to be a core solution. Improved judgment ability is enabled by stronger chain-of-thought reasoning, motivating the need to find the best recipes for training such models to think. In this work we introduce J1, a reinforcement learning approach to training such models. Our method converts both verifiable and non-verifiable prompts to judgment tasks with verifiable rewards that incentivize thinking and mitigate judgment bias. In particular, our approach outperforms all other existing 8B or 70B models when trained at those sizes, including models distilled from DeepSeek-R1. J1 also outperforms o1-mini, and even R1 on some benchmarks, despite training a smaller model. We provide analysis and ablations comparing Pairwise-J1 vs Pointwise-J1 models, offline vs online training recipes, reward strategies, seed prompts, and variations in thought length and content. We find that our models make better judgments by learning to outline evaluation criteria, comparing against self-generated reference answers, and re-evaluating the correctness of model responses.

The partial observability and stochasticity in multi-agent settings can be mitigated by accessing more information about others via communication. However, the coordination problem still exists since agents cannot communicate actual actions with each other at the same time due to the circular dependencies. In this paper, we propose a novel multi-level communication scheme, Sequential Communication (SeqComm). SeqComm treats agents asynchronously (the upper-level agents make decisions before the lower-level ones) and has two communication phases. In the negotiation phase, agents determine the priority of decision-making by communicating hidden states of observations and comparing the value of intention, obtained by modeling the environment dynamics. In the launching phase, the upper-level agents take the lead in making decisions and then communicate their actions with the lower-level agents. Theoretically, we prove the policies learned by SeqComm are guaranteed to improve monotonically and converge. Empirically, we show that SeqComm outperforms existing methods in various cooperative multi-agent tasks.

Autonomous driving involves multiple, often conflicting objectives such as safety, efficiency, and comfort. In reinforcement learning (RL), these objectives are typically combined through weighted summation, which collapses their relative priorities and often yields policies that violate safety-critical constraints. To overcome this limitation, we introduce the Preordered Multi-Objective MDP (Pr-MOMDP), which augments standard MOMDPs with a preorder over reward components. This structure enables reasoning about actions with respect to a hierarchy of objectives rather than a scalar signal. To make this structure actionable, we extend distributional RL with a novel pairwise comparison metric, Quantile Dominance (QD), that evaluates action return distributions without reducing them into a single statistic. Building on QD, we propose an algorithm for extracting optimal subsets, the subset of actions that remain non-dominated under each objective, which allows precedence information to shape both decision-making and training targets. Our framework is instantiated with Implicit Quantile Networks (IQN), establishing a concrete implementation while preserving compatibility with a broad class of distributional RL methods. Experiments in Carla show improved success rates, fewer collisions and off-road events, and deliver statistically more robust policies than IQN and ensemble-IQN baselines. By ensuring policies respect rewards preorder, our work advances safer, more reliable autonomous driving systems.

The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and intuitions: joint Shapley values measure a set of features' average contribution to a model's prediction. We prove the uniqueness of joint Shapley values, for any order of explanation. Results for games show that joint Shapley values present different insights from existing interaction indices, which assess the effect of a feature within a set of features. The joint Shapley values provide intuitive results in ML attribution problems. With binary features, we present a presence-adjusted global value that is more consistent with local intuitions than the usual approach.

Information is often stored in a distributed and proprietary form, and agents who own information are often self-interested and require incentives to reveal their information. Suitable mechanisms are required to elicit and aggregate such distributed information for decision making. In this paper, we use simulations to investigate the use of decision markets as mechanisms in a multi-agent learning system to aggregate distributed information for decision-making in a contextual bandit problem. The system utilises strictly proper decision scoring rules to assess the accuracy of probabilistic reports from agents, which allows agents to learn to solve the contextual bandit problem jointly. Our simulations show that our multi-agent system with distributed information can be trained as efficiently as a centralised counterpart with a single agent that receives all information. Moreover, we use our system to investigate scenarios with deterministic decision scoring rules which are not incentive compatible. We observe the emergence of more complex dynamics with manipulative behaviour, which agrees with existing theoretical analyses.

The evolution of Retrieval-Augmented Generation (RAG) has shifted from static retrieval pipelines to dynamic, agentic workflows where a central planner orchestrates multi-turn reasoning. However, existing paradigms face a critical dichotomy: they either optimize modules jointly within rigid, fixed-graph architectures, or empower dynamic planning while treating executors as frozen, black-box tools. We identify that this decoupled optimization creates a ``strategic-operational mismatch,'' where sophisticated planning strategies fail to materialize due to unadapted local executors, often leading to negative performance gains despite increased system complexity. In this paper, we propose JADE (Joint Agentic Dynamic Execution), a unified framework for the joint optimization of planning and execution within dynamic, multi-turn workflows. By modeling the system as a cooperative multi-agent team unified under a single shared backbone, JADE enables end-to-end learning driven by outcome-based rewards. This approach facilitates co-adaptation: the planner learns to operate within the capability boundaries of the executors, while the executors evolve to align with high-level strategic intent. Empirical results demonstrate that JADE transforms disjoint modules into a synergistic system, yielding remarkable performance improvements via joint optimization and enabling a flexible balance between efficiency and effectiveness through dynamic workflow orchestration.

The process of revising (or constructing) a policy at execution time -- known as decision-time planning -- has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

Feature fusion plays a crucial role in unconstrained face recognition where inputs (probes) comprise of a set of N low quality images whose individual qualities vary. Advances in attention and recurrent modules have led to feature fusion that can model the relationship among the images in the input set. However, attention mechanisms cannot scale to large N due to their quadratic complexity and recurrent modules suffer from input order sensitivity. We propose a two-stage feature fusion paradigm, Cluster and Aggregate, that can both scale to large N and maintain the ability to perform sequential inference with order invariance. Specifically, Cluster stage is a linear assignment of N inputs to M global cluster centers, and Aggregation stage is a fusion over M clustered features. The clustered features play an integral role when the inputs are sequential as they can serve as a summarization of past features. By leveraging the order-invariance of incremental averaging operation, we design an update rule that achieves batch-order invariance, which guarantees that the contributions of early image in the sequence do not diminish as time steps increase. Experiments on IJB-B and IJB-S benchmark datasets show the superiority of the proposed two-stage paradigm in unconstrained face recognition. Code and pretrained models are available in https://github.com/mk-minchul/caface

In multi-task reinforcement learning (RL) under Markov decision processes (MDPs), the presence of shared latent structures among multiple MDPs has been shown to yield significant benefits to the sample efficiency compared to single-task RL. In this paper, we investigate whether such a benefit can extend to more general sequential decision making problems, such as partially observable MDPs (POMDPs) and more general predictive state representations (PSRs). The main challenge here is that the large and complex model space makes it hard to identify what types of common latent structure of multi-task PSRs can reduce the model complexity and improve sample efficiency. To this end, we posit a joint model class for tasks and use the notion of eta-bracketing number to quantify its complexity; this number also serves as a general metric to capture the similarity of tasks and thus determines the benefit of multi-task over single-task RL. We first study upstream multi-task learning over PSRs, in which all tasks share the same observation and action spaces. We propose a provably efficient algorithm UMT-PSR for finding near-optimal policies for all PSRs, and demonstrate that the advantage of multi-task learning manifests if the joint model class of PSRs has a smaller eta-bracketing number compared to that of individual single-task learning. We also provide several example multi-task PSRs with small eta-bracketing numbers, which reap the benefits of multi-task learning. We further investigate downstream learning, in which the agent needs to learn a new target task that shares some commonalities with the upstream tasks via a similarity constraint. By exploiting the learned PSRs from the upstream, we develop a sample-efficient algorithm that provably finds a near-optimal policy.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

Deep reinforcement learning (RL) has been applied extensively to solve complex decision-making problems. In many real-world scenarios, tasks often have several conflicting objectives and may require multiple agents to cooperate, which are the multi-objective multi-agent decision-making problems. However, only few works have been conducted on this intersection. Existing approaches are limited to separate fields and can only handle multi-agent decision-making with a single objective, or multi-objective decision-making with a single agent. In this paper, we propose MO-MIX to solve the multi-objective multi-agent reinforcement learning (MOMARL) problem. Our approach is based on the centralized training with decentralized execution (CTDE) framework. A weight vector representing preference over the objectives is fed into the decentralized agent network as a condition for local action-value function estimation, while a mixing network with parallel architecture is used to estimate the joint action-value function. In addition, an exploration guide approach is applied to improve the uniformity of the final non-dominated solutions. Experiments demonstrate that the proposed method can effectively solve the multi-objective multi-agent cooperative decision-making problem and generate an approximation of the Pareto set. Our approach not only significantly outperforms the baseline method in all four kinds of evaluation metrics, but also requires less computational cost.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.

We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where multiple agents cooperate via communication through a central server. We propose a provably efficient algorithm based on value iteration that enable asynchronous communication while ensuring the advantage of cooperation with low communication overhead. With linear function approximation, we prove that our algorithm enjoys an mathcal{O}(d^{3/2}H^2K) regret with mathcal{O}(dHM^2) communication complexity, where d is the feature dimension, H is the horizon length, M is the total number of agents, and K is the total number of episodes. We also provide a lower bound showing that a minimal Omega(dM) communication complexity is required to improve the performance through collaboration.

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect-information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games and yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Reinforcement learning (RL) tasks are typically framed as Markov Decision Processes (MDPs), assuming that decisions are made at fixed time intervals. However, many applications of great importance, including healthcare, do not satisfy this assumption, yet they are commonly modelled as MDPs after an artificial reshaping of the data. In addition, most healthcare (and similar) problems are offline by nature, allowing for only retrospective studies. To address both challenges, we begin by discussing the Semi-MDP (SMDP) framework, which formally handles actions of variable timings. We next present a formal way to apply SMDP modifications to nearly any given value-based offline RL method. We use this theory to introduce three SMDP-based offline RL algorithms, namely, SDQN, SDDQN, and SBCQ. We then experimentally demonstrate that only these SMDP-based algorithms learn the optimal policy in variable-time environments, whereas their MDP counterparts do not. Finally, we apply our new algorithms to a real-world offline dataset pertaining to warfarin dosing for stroke prevention and demonstrate similar results.

Algorithms increasingly serve as information mediators--from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g. an LLM) controls the information structure of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (altruistic planner) or to induce a specific action the planner prefers (biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. We prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. Notably, in some regimes the biased planner intentionally obfuscates the agents' signals. Even under stringent transparency constraints--information parity with individuals, no lying or cherry-picking, and full observability--we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning consistent with the cognitive patterns of both humans and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators.

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-world problem.

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.

Long-horizon Flexible Job-Shop Scheduling~(FJSP) presents a formidable combinatorial challenge due to complex, interdependent decisions spanning extended time horizons. While learning-based Rolling Horizon Optimization~(RHO) has emerged as a promising paradigm to accelerate solving by identifying and fixing invariant operations, its effectiveness is hindered by the structural complexity of FJSP. Existing methods often fail to capture intricate graph-structured dependencies and ignore the asymmetric costs of prediction errors, in which misclassifying critical-path operations is significantly more detrimental than misclassifying non-critical ones. Furthermore, dynamic shifts in predictive confidence during the rolling process make static pruning thresholds inadequate. To address these limitations, we propose Graph-RHO, a novel critical-path-aware graph-based RHO framework. First, we introduce a topology-aware heterogeneous graph network that encodes subproblems as operation-machine graphs with multi-relational edges, leveraging edge-feature-aware message passing to predict operation stability. Second, we incorporate a critical-path-aware mechanism that injects inductive biases during training to distinguish highly sensitive bottleneck operations from robust ones. Third, we devise an adaptive thresholding strategy that dynamically calibrates decision boundaries based on online uncertainty estimation to align model predictions with the solver's search space. Extensive experiments on standard benchmarks demonstrate that Graph-RHO establishes a new state of the art in solution quality and computational efficiency. Remarkably, it exhibits exceptional zero-shot generalization, reducing solve time by over 30\% on large-scale instances (2000 operations) while achieving superior solution quality. Our code is available https://github.com/IntelliSensing/Graph-RHO{here}.

POMDPs capture a broad class of decision making problems, but hardness results suggest that learning is intractable even in simple settings due to the inherent partial observability. However, in many realistic problems, more information is either revealed or can be computed during some point of the learning process. Motivated by diverse applications ranging from robotics to data center scheduling, we formulate a Hindsight Observable Markov Decision Process (HOMDP) as a POMDP where the latent states are revealed to the learner in hindsight and only during training. We introduce new algorithms for the tabular and function approximation settings that are provably sample-efficient with hindsight observability, even in POMDPs that would otherwise be statistically intractable. We give a lower bound showing that the tabular algorithm is optimal in its dependence on latent state and observation cardinalities.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose an efficient and robust value estimator and illustrate its effectiveness through extensive simulations and analysis of real data from a world-leading short-video platform.

Recent advances in large-scale language models (LLMs) have made multi-agent architectures attractive for challenging reasoning tasks. However, many existing systems rely on stochastic routing or ad-hoc heuristics, making their behavior difficult to reproduce and their decision process hard to interpret. We propose ORCH, a deterministic coordination framework for discrete-choice reasoning that orchestrates heterogeneous LLMs. ORCH follows a ``many analyses, one decision'' paradigm: multiple base models independently produce structured analyses, and a dedicated merge agent outputs the final choice. The framework uses fixed rules for task decomposition and answer aggregation, keeping the pipeline predictable, reproducible, and training-free. Determinism here refers to fixed routing and aggregation rules under a fixed evaluation protocol, rather than strict bit-level reproducibility across deployments. To exploit model complementarity, we optionally introduce an EMA-guided router that updates agent selection using historical accuracy, latency, or cost; since it relies on answer-based feedback, it is mainly intended for benchmarking, controlled evaluation, or delayed-feedback settings. Experiments on MMLU, MMLU-Pro, and GSM8K show that ORCH consistently outperforms single-model baselines and a majority-vote ensemble. On MMLU-Pro, ORCH improves accuracy by over 10 points compared to the strongest baseline, and on GSM8K it yields gains exceeding 50 points; McNemar tests confirm statistical significance. The EMA router provides an additional 0.7--2.0 point accuracy boost, and ablations show that both multi-agent collaboration and routing contribute substantially. Overall, ORCH offers a practical path toward controllable, interpretable, and deployment-ready LLM-based agent systems for discrete-choice reasoning.

Agreement Technologies refer to open computer systems in which autonomous software agents interact with one another, typically on behalf of humans, in order to come to mutually acceptable agreements. With the advance of AI systems in recent years, it has become apparent that such agreements, in order to be acceptable to the involved parties, must remain aligned with ethical principles and moral values. However, this is notoriously difficult to ensure, especially as different human users (and their software agents) may hold different value systems, i.e. they may differently weigh the importance of individual moral values. Furthermore, it is often hard to specify the precise meaning of a value in a particular context in a computational manner. Methods to estimate value systems based on human-engineered specifications, e.g. based on value surveys, are limited in scale due to the need for intense human moderation. In this article, we propose a novel method to automatically learn value systems from observations and human demonstrations. In particular, we propose a formal model of the value system learning problem, its instantiation to sequential decision-making domains based on multi-objective Markov decision processes, as well as tailored preference-based and inverse reinforcement learning algorithms to infer value grounding functions and value systems. The approach is illustrated and evaluated by two simulated use cases.

This study investigates large language model (LLM) -based multi-agent systems (MASs) as a promising approach to inventory management, which is a key component of supply chain management. Although these systems have gained considerable attention for their potential to address the challenges associated with typical inventory management methods, key uncertainties regarding their effectiveness persist. Specifically, it is unclear whether LLM-based MASs can consistently derive optimal ordering policies and adapt to diverse supply chain scenarios. To address these questions, we examine an LLM-based MAS with a fixed-ordering strategy prompt that encodes the stepwise processes of the problem setting and a safe-stock strategy commonly used in inventory management. Our empirical results demonstrate that, even without detailed prompt adjustments, an LLM-based MAS can determine optimal ordering decisions in a restricted scenario. To enhance adaptability, we propose a novel agent called AIM-RM, which leverages similar historical experiences through similarity matching. Our results show that AIM-RM outperforms benchmark methods across various supply chain scenarios, highlighting its robustness and adaptability.

Multi-Agent Reinforcement Learning (MARL) based Multi-Agent Path Finding (MAPF) has recently gained attention due to its efficiency and scalability. Several MARL-MAPF methods choose to use communication to enrich the information one agent can perceive. However, existing works still struggle in structured environments with high obstacle density and a high number of agents. To further improve the performance of the communication-based MARL-MAPF solvers, we propose a new method, Ensembling Prioritized Hybrid Policies (EPH). We first propose a selective communication block to gather richer information for better agent coordination within multi-agent environments and train the model with a Q learning-based algorithm. We further introduce three advanced inference strategies aimed at bolstering performance during the execution phase. First, we hybridize the neural policy with single-agent expert guidance for navigating conflict-free zones. Secondly, we propose Q value-based methods for prioritized resolution of conflicts as well as deadlock situations. Finally, we introduce a robust ensemble method that can efficiently collect the best out of multiple possible solutions. We empirically evaluate EPH in complex multi-agent environments and demonstrate competitive performance against state-of-the-art neural methods for MAPF. We open-source our code at https://github.com/ai4co/eph-mapf.

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.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

Generative Reward Models (GRMs) have attracted considerable research interest in reward modeling due to their interpretability, inference-time scalability, and potential for refinement through reinforcement learning (RL). However, widely used pairwise GRMs create a computational bottleneck when integrated with RL algorithms such as Group Relative Policy Optimization (GRPO). This bottleneck arises from two factors: (i) the O(n^2) time complexity of pairwise comparisons required to obtain relative scores, and (ii) the computational overhead of repeated sampling or additional chain-of-thought (CoT) reasoning to improve performance. To address the first factor, we propose Intergroup Relative Preference Optimization (IRPO), a novel RL framework that incorporates the well-established Bradley-Terry model into GRPO. By generating a pointwise score for each response, IRPO enables efficient evaluation of arbitrarily many candidates during RL training while preserving interpretability and fine-grained reward signals. Experimental results demonstrate that IRPO achieves state-of-the-art (SOTA) performance among pointwise GRMs across multiple benchmarks, with performance comparable to that of current leading pairwise GRMs. Furthermore, we show that IRPO significantly outperforms pairwise GRMs in post-training evaluations.

We propose a framework to learn to schedule a job-shop problem (JSSP) using a graph neural network (GNN) and reinforcement learning (RL). We formulate the scheduling process of JSSP as a sequential decision-making problem with graph representation of the state to consider the structure of JSSP. In solving the formulated problem, the proposed framework employs a GNN to learn that node features that embed the spatial structure of the JSSP represented as a graph (representation learning) and derive the optimum scheduling policy that maps the embedded node features to the best scheduling action (policy learning). We employ Proximal Policy Optimization (PPO) based RL strategy to train these two modules in an end-to-end fashion. We empirically demonstrate that the GNN scheduler, due to its superb generalization capability, outperforms practically favored dispatching rules and RL-based schedulers on various benchmark JSSP. We also confirmed that the proposed framework learns a transferable scheduling policy that can be employed to schedule a completely new JSSP (in terms of size and parameters) without further training.

We focus on a simple, one-dimensional collective decision problem (often referred to as the facility location problem) and explore issues of strategyproofness and proportionality-based fairness. We introduce and analyze a hierarchy of proportionality-based fairness axioms of varying strength: Individual Fair Share (IFS), Unanimous Fair Share (UFS), Proportionality (as in Freeman et al, 2021), and Proportional Fairness (PF). For each axiom, we characterize the family of mechanisms that satisfy the axiom and strategyproofness. We show that imposing strategyproofness renders many of the axioms to be equivalent: the family of mechanisms that satisfy proportionality, unanimity, and strategyproofness is equivalent to the family of mechanisms that satisfy UFS and strategyproofness, which, in turn, is equivalent to the family of mechanisms that satisfy PF and strategyproofness. Furthermore, there is a unique such mechanism: the Uniform Phantom mechanism, which is studied in Freeman et al. (2021). We also characterize the outcomes of the Uniform Phantom mechanism as the unique (pure) equilibrium outcome for any mechanism that satisfies continuity, strict monotonicity, and UFS. Finally, we analyze the approximation guarantees, in terms of optimal social welfare and minimum total cost, obtained by mechanisms that are strategyproof and satisfy each proportionality-based fairness axiom. We show that the Uniform Phantom mechanism provides the best approximation of the optimal social welfare (and also minimum total cost) among all mechanisms that satisfy UFS.

Two common approaches to sequential decision-making are AI planning (AIP) and reinforcement learning (RL). Each has strengths and weaknesses. AIP is interpretable, easy to integrate with symbolic knowledge, and often efficient, but requires an up-front logical domain specification and is sensitive to noise; RL only requires specification of rewards and is robust to noise but is sample inefficient and not easily supplied with external knowledge. We propose an integrative approach that combines high-level planning with RL, retaining interpretability, transfer, and efficiency, while allowing for robust learning of the lower-level plan actions. Our approach defines options in hierarchical reinforcement learning (HRL) from AIP operators by establishing a correspondence between the state transition model of AI planning problem and the abstract state transition system of a Markov Decision Process (MDP). Options are learned by adding intrinsic rewards to encourage consistency between the MDP and AIP transition models. We demonstrate the benefit of our integrated approach by comparing the performance of RL and HRL algorithms in both MiniGrid and N-rooms environments, showing the advantage of our method over the existing ones.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve Oleft(Delta^{1/4}T^{3/4}right) regret when the degree of nonstationarity, as measured by total variation Delta, is known, and Oleft(Delta^{1/5}T^{4/5}right) regret when Delta is unknown, where T is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

Multi-agent reinforcement learning shines as the pinnacle of multi-agent systems, conquering intricate real-world challenges, fostering collaboration and coordination among agents, and unleashing the potential for intelligent decision-making across domains. However, training a multi-agent reinforcement learning network is a formidable endeavor, demanding substantial computational resources to interact with diverse environmental variables, extract state representations, and acquire decision-making knowledge. The recent breakthroughs in large-scale pre-trained models ignite our curiosity: Can we uncover shared knowledge in multi-agent reinforcement learning and leverage pre-trained models to expedite training for future tasks? Addressing this issue, we present an innovative multi-task learning approach that aims to extract and harness common decision-making knowledge, like cooperation and competition, across different tasks. Our approach involves concurrent training of multiple multi-agent tasks, with each task employing independent front-end perception layers while sharing back-end decision-making layers. This effective decoupling of state representation extraction from decision-making allows for more efficient training and better transferability. To evaluate the efficacy of our proposed approach, we conduct comprehensive experiments in two distinct environments: the StarCraft Multi-agent Challenge (SMAC) and the Google Research Football (GRF) environments. The experimental results unequivocally demonstrate the smooth transferability of the shared decision-making network to other tasks, thereby significantly reducing training costs and improving final performance. Furthermore, visualizations authenticate the presence of general multi-agent decision-making knowledge within the shared network layers, further validating the effectiveness of our approach.

In this paper, we present a novel method for reliable frontier selection in Zero-Shot Object Goal Navigation (ZS-OGN), enhancing robotic navigation systems with foundation models to improve commonsense reasoning in indoor environments. Our approach introduces a multi-expert decision framework to address the nonsensical or irrelevant reasoning often seen in foundation model-based systems. The method comprises two key components: Diversified Expert Frontier Analysis (DEFA) and Consensus Decision Making (CDM). DEFA utilizes three expert models: furniture arrangement, room type analysis, and visual scene reasoning, while CDM aggregates their outputs, prioritizing unanimous or majority consensus for more reliable decisions. Demonstrating state-of-the-art performance on the RoboTHOR and HM3D datasets, our method excels at navigating towards untrained objects or goals and outperforms various baselines, showcasing its adaptability to dynamic real-world conditions and superior generalization capabilities.

We consider non-clairvoyant scheduling with online precedence constraints, where an algorithm is oblivious to any job dependencies and learns about a job only if all of its predecessors have been completed. Given strong impossibility results in classical competitive analysis, we investigate the problem in a learning-augmented setting, where an algorithm has access to predictions without any quality guarantee. We discuss different prediction models: novel problem-specific models as well as general ones, which have been proposed in previous works. We present lower bounds and algorithmic upper bounds for different precedence topologies, and thereby give a structured overview on which and how additional (possibly erroneous) information helps for designing better algorithms. Along the way, we also improve bounds on traditional competitive ratios for existing algorithms.

Large Language Model (LLM) agents deployed for real-world tasks face a fundamental dilemma: user requests are underspecified, yet agents must decide whether to act on incomplete information or interrupt users for clarification. Existing approaches either rely on brittle confidence thresholds that require task-specific tuning, or fail to account for the varying stakes of different decisions. We introduce a decision-theoretic framework that resolves this trade-off through the Value of Information (VoI), enabling agents to dynamically weigh the expected utility gain from asking questions against the cognitive cost imposed on users. Our inference-time method requires no hyperparameter tuning and adapts seamlessly across contexts-from casual games to medical diagnosis. Experiments across four diverse domains (20 Questions, medical diagnosis, flight booking, and e-commerce) show that VoI consistently matches or exceeds the best manually-tuned baselines, achieving up to 1.36 utility points higher in high-cost settings. This work provides a parameter-free framework for adaptive agent communication that explicitly balances task risk, query ambiguity, and user effort.

LLMs are increasingly being used for complex problems which are not necessarily resolved in a single response, but require interacting with an environment to acquire information. In these scenarios, LLMs must reason about inherent cost-uncertainty tradeoffs in when to stop exploring and commit to an answer. For instance, on a programming task, an LLM should test a generated code snippet if it is uncertain about the correctness of that code; the cost of writing a test is nonzero, but typically lower than the cost of making a mistake. In this work, we show that we can induce LLMs to explicitly reason about balancing these cost-uncertainty tradeoffs, then perform more optimal environment exploration. We formalize multiple tasks, including information retrieval and coding, as sequential decision-making problems under uncertainty. Each problem has latent environment state that can be reasoned about via a prior which is passed to the LLM agent. We introduce a framework called Calibrate-Then-Act (CTA), where we feed the LLM this additional context to enable it to act more optimally. This improvement is preserved even under RL training of both the baseline and CTA. Our results on information-seeking QA and on a simplified coding task show that making cost-benefit tradeoffs explicit with CTA can help agents discover more optimal decision-making strategies.

Combinatorial optimization problems involving multiple agents are notoriously challenging due to their NP-hard nature and the necessity for effective agent coordination. Despite advancements in learning-based methods, existing approaches often face critical limitations, including suboptimal agent coordination, poor generalizability, and high computational latency. To address these issues, we propose Parallel AutoRegressive Combinatorial Optimization (PARCO), a reinforcement learning framework designed to construct high-quality solutions for multi-agent combinatorial tasks efficiently. To this end, PARCO integrates three key components: (1) transformer-based communication layers to enable effective agent collaboration during parallel solution construction, (2) a multiple pointer mechanism for low-latency, parallel agent decision-making, and (3) priority-based conflict handlers to resolve decision conflicts via learned priorities. We evaluate PARCO in multi-agent vehicle routing and scheduling problems where our approach outperforms state-of-the-art learning methods and demonstrates strong generalization ability and remarkable computational efficiency. Code available at: https://github.com/ai4co/parco.

We study an online learning problem in general-sum Stackelberg games, where players act in a decentralized and strategic manner. We study two settings depending on the type of information for the follower: (1) the limited information setting where the follower only observes its own reward, and (2) the side information setting where the follower has extra side information about the leader's reward. We show that for the follower, myopically best responding to the leader's action is the best strategy for the limited information setting, but not necessarily so for the side information setting -- the follower can manipulate the leader's reward signals with strategic actions, and hence induce the leader's strategy to converge to an equilibrium that is better off for itself. Based on these insights, we study decentralized online learning for both players in the two settings. Our main contribution is to derive last-iterate convergence and sample complexity results in both settings. Notably, we design a new manipulation strategy for the follower in the latter setting, and show that it has an intrinsic advantage against the best response strategy. Our theories are also supported by empirical results.

Coopetition refers to simultaneous cooperation and competition among actors wherein actors 'cooperate to grow the pie and compete to split it up.' Modern socio-technical systems are characterized by strategic coopetition wherein actors concomitantly cooperate to create value and compete to capture it. While conceptual modeling languages such as i* provide rich qualitative representations of strategic dependencies, they lack mechanisms for quantitative analysis of dynamic trade-offs. Conversely, classical game theory offers mathematical rigor but strips away contextual richness. This report bridges this gap by developing computational foundations that formalize two critical dimensions of coopetition: interdependence and complementarity. We ground interdependence in i* structural dependency analysis, translating depender-dependee-dependum relationships into quantitative interdependence coefficients via a structured translation framework. We formalize complementarity following Brandenburger and Nalebuff's Added Value concept, modeling synergistic value creation with validated parameterization. We integrate structural dependencies with bargaining power in value appropriation and introduce a game-theoretic formulation where Nash Equilibrium incorporates structural interdependence. Validation combines over 22,000 experimental trials across power and logarithmic specifications with the Samsung-Sony S-LCD joint venture (2004-2011). Under strict historical alignment scoring, logarithmic specifications achieve 58/60 compared to power functions (46/60), producing realistic 41% cooperation increases aligning with documented S-LCD patterns while power functions produce 166% increases exceeding realistic bounds. Statistical significance confirmed at p < 0.001, Cohen's d > 9.

Large language models excel at reasoning but lack key aspects of introspection, including anticipating their own success and the computation required to achieve it. Humans use real-time introspection to decide how much effort to invest, when to make multiple attempts, when to stop, and when to signal success or failure. Without this, LLMs struggle to make intelligent meta-cognition decisions. Test-time scaling methods like Best-of-N drive up cost and latency by using a fixed budget of samples regardless of the marginal benefit of each one at any point in generation, and the absence of confidence signals can mislead people, prevent appropriate escalation to better tools, and undermine trustworthiness. Learned verifiers or reward models can provide confidence estimates, but do not enable adaptive inference and add substantial cost by requiring extra models or forward passes. We present ZIP-RC, which equips models with zero-overhead introspective predictions of reward and cost. At every token, ZIP-RC reuses reserved or unused logits in the same forward pass as next-token prediction to output a joint distribution over final reward and remaining length -- no extra models, architecture change, or inference overhead. This full joint distribution is used to compute a sampling utility which is the linear combination of the expected maximum reward, total compute, and latency of set of samples if generated to completion. During inference, we maximize this utility with meta-actions that determine which prefix of tokens to continue or initiate sampling from. On mixed-difficulty mathematical benchmarks, ZIP-RC improves accuracy by up to 12% over majority voting at equal or lower average cost, and traces smooth Pareto frontiers between quality, compute, and latency. By providing real-time reward-cost introspection, ZIP-RC enables adaptive, efficient reasoning.

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent this structure by a weighted directed graph, where the edge weights are related to the quality of the feedback shared by the connected nodes. Our main contribution is an efficient algorithm that guarantees a regret of O(α^* T) after T rounds, where α^* is a novel graph property that we call the effective independence number. Our algorithm is completely parameter-free and does not require knowledge (or even estimation) of α^*. For the special case of binary edge weights, our setting reduces to the partial-observability models of Mannor and Shamir (2011) and Alon et al. (2013) and our algorithm recovers the near-optimal regret bounds.

Decision Transformer (DT) is an innovative algorithm leveraging recent advances of the transformer architecture in reinforcement learning (RL). However, a notable limitation of DT is its reliance on recalling trajectories from datasets, losing the capability to seamlessly stitch sub-optimal trajectories together. In this work we introduce a general sequence modeling framework for studying sequential decision making through the lens of Hierarchical RL. At the time of making decisions, a high-level policy first proposes an ideal prompt for the current state, a low-level policy subsequently generates an action conditioned on the given prompt. We show DT emerges as a special case of this framework with certain choices of high-level and low-level policies, and discuss the potential failure of these choices. Inspired by these observations, we study how to jointly optimize the high-level and low-level policies to enable the stitching ability, which further leads to the development of new offline RL algorithms. Our empirical results clearly show that the proposed algorithms significantly surpass DT on several control and navigation benchmarks. We hope our contributions can inspire the integration of transformer architectures within the field of RL.

Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn epsilon-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound mathcal{O}(H(A_{X}+B_{Y})/epsilon^2) on the required number of realizations to learn these strategies with high probability, where H is the length of the game, A_{X} and B_{Y} are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs mathcal{O}(H^2(A_{X}+B_{Y})/epsilon^2) realizations without this requirement by progressively adapting the regularization to the observations.

Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential for general tasks like mathematics and coding. Consequently, numerous works have leveraged reinforcement learning (RL) to elicit the reasoning capability of dLLMs. In this paper, we reveal a counter-intuitive reality: arbitrary order generation, in its current form, narrows rather than expands the reasoning boundary of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of the solution space. This observation challenges the premise of existing RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning is better elicited by intentionally forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, JustGRPO, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs. Project page: https://nzl-thu.github.io/the-flexibility-trap

Value function factorization has achieved great success in multi-agent reinforcement learning by optimizing joint action-value functions through the maximization of factorized per-agent utilities. To ensure Individual-Global-Maximum property, existing works often focus on value factorization using monotonic functions, which are known to result in restricted representation expressiveness. In this paper, we analyze the limitations of monotonic factorization and present ConcaveQ, a novel non-monotonic value function factorization approach that goes beyond monotonic mixing functions and employs neural network representations of concave mixing functions. Leveraging the concave property in factorization, an iterative action selection scheme is developed to obtain optimal joint actions during training. It is used to update agents' local policy networks, enabling fully decentralized execution. The effectiveness of the proposed ConcaveQ is validated across scenarios involving multi-agent predator-prey environment and StarCraft II micromanagement tasks. Empirical results exhibit significant improvement of ConcaveQ over state-of-the-art multi-agent reinforcement learning approaches.

Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a latent preference state matrix, where the spread between an agent's internal ask price (the unconditional maximum) and the market's best bid (the reachable maximum) creates a structural liquidity constraint. We establish a Threshold Impossibility Theorem showing that linear compensation cannot close these spreads unless it induces a categorical identity shift. A dynamic discrete choice execution model further demonstrates that matches occur only when the market to book ratio crosses a time decaying liquidity threshold, analogous to order execution under inventory pressure. Numerical experiments validate persistent slippage, regional invariance of preference orderings, and high tier zero spread executions. The model provides a unified microstructure explanation for matching failures, compensation inefficiency, and post match regret in illiquid order driven environments.

Tree search has become as a representative framework for test-time reasoning with large language models (LLMs), exemplified by methods such as Tree-of-Thought and Monte Carlo Tree Search that explore multiple reasoning paths. However, it remains difficult to provide instant and reliable quantitative assessments of intermediate reasoning step quality, and extensive path exploration is computationally costly. To address this, we propose Mutual Information Tree Search (MITS), a novel framework that guides reasoning with information-theoretic principles. MITS introduces an effective scoring function based on pointwise mutual information (PMI), which enables step-wise evaluation of reasoning paths and search tree expansion via beam search without expensive look-ahead simulations, achieving superior reasoning performances while maintaining computational efficiency. The framework is complemented by an entropy-based dynamic sampling strategy that adaptively allocates computational resources to uncertain reasoning steps where exploration is most beneficial. For final prediction, MITS employs a weighted voting scheme that combines PMI scores with prediction consensus. Through comprehensive experiments on diverse reasoning benchmarks, MITS consistently surpasses baseline methods, establishing a principled and efficient framework for LLM reasoning.

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero'th order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes. Our results are the first to target simple regret definitions in adversarial scenarios unveiling a challenge that has been rarely considered in prior work.

Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence and Wasserstein distance.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Large language models (LLMs) are increasingly deployed as autonomous decision agents in settings with asymmetric error costs: hiring (missed talent vs wasted interviews), medical triage (missed emergencies vs unnecessary escalation), and fraud detection (approved fraud vs declined legitimate payments). The dominant design queries a single LLM for a posterior over states, thresholds "confidence," and acts; we prove this is inadequate for sequential decisions with costs. We propose a Bayesian, cost-aware multi-LLM orchestration framework that treats LLMs as approximate likelihood models rather than classifiers. For each candidate state, we elicit likelihoods via contrastive prompting, aggregate across diverse models with robust statistics, and update beliefs with Bayes rule under explicit priors as new evidence arrives. This enables coherent belief updating, expected-cost action selection, principled information gathering via value of information, and fairness gains via ensemble bias mitigation. In resume screening with costs of 40000 USD per missed hire, 2500 USD per interview, and 150 USD per phone screen, experiments on 1000 resumes using five LLMs (GPT-4o, Claude 4.5 Sonnet, Gemini Pro, Grok, DeepSeek) reduce total cost by 294000 USD (34 percent) versus the best single-LLM baseline and improve demographic parity by 45 percent (max group gap 22 to 5 percentage points). Ablations attribute 51 percent of savings to multi-LLM aggregation, 43 percent to sequential updating, and 20 percent to disagreement-triggered information gathering, consistent with the theoretical benefits of correct probabilistic foundations.

Knowing when to answer or refuse is crucial for safe and reliable decision-making language agents. Although prior work has introduced refusal strategies to boost LMs' reliability, how these models adapt their decisions to different risk levels remains underexplored. We formalize the task of risk-aware decision-making, expose critical weaknesses in existing LMs, and propose skill-decomposition solutions to mitigate them. Our findings show that even cutting-edge LMs--both regular and reasoning models--still require explicit prompt chaining to handle the task effectively, revealing the challenges that must be overcome to achieve truly autonomous decision-making agents.

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.

To optimally coordinate with others in cooperative games, it is often crucial to have information about one's collaborators: successful driving requires understanding which side of the road to drive on. However, not every feature of collaborators is strategically relevant: the fine-grained acceleration of drivers may be ignored while maintaining optimal coordination. We show that there is a well-defined dichotomy between strategically relevant and irrelevant information. Moreover, we show that, in dynamic games, this dichotomy has a compact representation that can be efficiently computed via a Bellman backup operator. We apply this algorithm to analyze the strategically relevant information for tasks in both a standard and a partially observable version of the Overcooked environment. Theoretical and empirical results show that our algorithms are significantly more efficient than baselines. Videos are available at https://minknowledge.github.io.

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T^{2/3}-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

The best-of-both-worlds paradigm advocates an approach that achieves desirable properties both ex-ante and ex-post. We launch a best-of-both-worlds fairness perspective for the important social choice setting of approval-based committee voting. To this end, we initiate work on ex-ante proportional representation properties in this domain and formalize a hierarchy of notions including Individual Fair Share (IFS), Unanimous Fair Share (UFS), Group Fair Share (GFS), and their stronger variants. We establish their compatibility with well-studied ex-post concepts such as extended justified representation (EJR) and fully justified representation (FJR). Our first main result is a polynomial-time algorithm that simultaneously satisfies ex-post EJR, ex-ante GFS and ex-ante Strong UFS. Subsequently, we strengthen our ex-post guarantee to FJR and present an algorithm that outputs a lottery which is ex-post FJR and ex-ante Strong UFS, but does not run in polynomial time.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

RAG systems consist of multiple modules to work together. However, these modules are usually separately trained. We argue that a system like RAG that incorporates multiple modules should be jointly optimized to achieve optimal performance. To demonstrate this, we design a specific pipeline called SmartRAG that includes a policy network and a retriever. The policy network can serve as 1) a decision maker that decides when to retrieve, 2) a query rewriter to generate a query most suited to the retriever, and 3) an answer generator that produces the final response with/without the observations. We then propose to jointly optimize the whole system using a reinforcement learning algorithm, with the reward designed to encourage the system to achieve the best performance with minimal retrieval cost. When jointly optimized, all the modules can be aware of how other modules are working and thus find the best way to work together as a complete system. Empirical results demonstrate that the jointly optimized SmartRAG can achieve better performance than separately optimized counterparts.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Fleets of robo-taxis offering on-demand transportation services, commonly known as Autonomous Mobility-on-Demand (AMoD) systems, hold significant promise for societal benefits, such as reducing pollution, energy consumption, and urban congestion. However, orchestrating these systems at scale remains a critical challenge, with existing coordination algorithms often failing to exploit the systems' full potential. This work introduces a novel decision-making framework that unites mathematical modeling with data-driven techniques. In particular, we present the AMoD coordination problem through the lens of reinforcement learning and propose a graph network-based framework that exploits the main strengths of graph representation learning, reinforcement learning, and classical operations research tools. Extensive evaluations across diverse simulation fidelities and scenarios demonstrate the flexibility of our approach, achieving superior system performance, computational efficiency, and generalizability compared to prior methods. Finally, motivated by the need to democratize research efforts in this area, we release publicly available benchmarks, datasets, and simulators for network-level coordination alongside an open-source codebase designed to provide accessible simulation platforms and establish a standardized validation process for comparing methodologies. Code available at: https://github.com/StanfordASL/RL4AMOD

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithm termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization-based EpsMix algorithm is also proposed and shown to achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

Decision-making, a complicated task requiring various types of abilities, presents an excellent framework for assessing Large Language Models (LLMs). Our research investigates LLMs' decision-making capabilities through the lens of a well-established field, Game Theory. We focus specifically on games that support the participation of more than two agents simultaneously. Subsequently, we introduce our framework, GAMA-Bench, including eight classical multi-agent games. We design a scoring scheme to assess a model's performance in these games quantitatively. Through GAMA-Bench, we investigate LLMs' robustness, generalizability, and enhancement strategies. Results reveal that while GPT-3.5 shows satisfying robustness, its generalizability is relatively limited. However, its performance can be improved through approaches such as Chain-of-Thought. Additionally, we conduct evaluations across various LLMs and find that GPT-4 outperforms other models on GAMA-Bench, achieving a score of 60.5. Moreover, Gemini-1.0-Pro and GPT-3.5 (0613, 1106, 0125) demonstrate similar intelligence on GAMA-Bench. The code and experimental results are made publicly available via https://github.com/CUHK-ARISE/GAMABench.

Interpretability is a pressing issue for decision systems. Many post hoc methods have been proposed to explain the predictions of a single machine learning model. However, business processes and decision systems are rarely centered around a unique model. These systems combine multiple models that produce key predictions, and then apply decision rules to generate the final decision. To explain such decisions, we propose the Semi-Model-Agnostic Contextual Explainer (SMACE), a new interpretability method that combines a geometric approach for decision rules with existing interpretability methods for machine learning models to generate an intuitive feature ranking tailored to the end user. We show that established model-agnostic approaches produce poor results on tabular data in this setting, in particular giving the same importance to several features, whereas SMACE can rank them in a meaningful way.

Multi-agent systems composed of large generative models are rapidly moving from laboratory prototypes to real-world deployments, where they jointly plan, negotiate, and allocate shared resources to solve complex tasks. While such systems promise unprecedented scalability and autonomy, their collective interaction also gives rise to failure modes that cannot be reduced to individual agents. Understanding these emergent risks is therefore critical. Here, we present a pioneer study of such emergent multi-agent risk in workflows that involve competition over shared resources (e.g., computing resources or market share), sequential handoff collaboration (where downstream agents see only predecessor outputs), collective decision aggregation, and others. Across these settings, we observe that such group behaviors arise frequently across repeated trials and a wide range of interaction conditions, rather than as rare or pathological cases. In particular, phenomena such as collusion-like coordination and conformity emerge with non-trivial frequency under realistic resource constraints, communication protocols, and role assignments, mirroring well-known pathologies in human societies despite no explicit instruction. Moreover, these risks cannot be prevented by existing agent-level safeguards alone. These findings expose the dark side of intelligent multi-agent systems: a social intelligence risk where agent collectives, despite no instruction to do so, spontaneously reproduce familiar failure patterns from human societies.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can carry greater risks than others in real-world long-tailed problems. For example, misclassifying patients (a tail class) as healthy individuals (a head class) entails far more serious consequences than the reverse scenario. To address this critical issue, we introduce Making Reliable and Flexible Decisions in Long-tailed Classification (RF-DLC), a novel framework aimed at reliable predictions in long-tailed problems. Leveraging Bayesian Decision Theory, we introduce an integrated gain to seamlessly combine long-tailed data distributions and the decision-making procedure. We further propose an efficient variational optimization strategy for the decision risk objective. Our method adapts readily to diverse utility matrices, which can be designed for specific tasks, ensuring its flexibility for different problem settings. In empirical evaluation, we design a new metric, False Head Rate, to quantify tail-sensitivity risk, along with comprehensive experiments on multiple real-world tasks, including large-scale image classification and uncertainty quantification, to demonstrate the reliability and flexibility of our method.

Effective decision-making in Large Language Models (LLMs) is essential for handling intricate tasks. However, existing approaches prioritize performance but often overlook the balance between effectiveness and computational cost. To address this, we first introduce the 3E Criteria to systematically assess the cost-effectiveness of search strategies, revealing that existing methods often trade significant efficiency for marginal performance gains. To improve LLM decision-making while maintaining efficiency, we propose the Speculative Reward Model (SRM), a plug-and-play framework that seamlessly integrates with existing search strategies. Specifically, SRM employs an external reward assigner to predict optimal actions, reducing reliance on LLMs' internal self-evaluation. And a speculative verification mechanism is used to prune suboptimal choices and guide the search toward more promising steps. We evaluate SRM on several complex decision-making tasks including mathematical reasoning, planning and numerical reasoning in specialized domains. Experimental results show that SRM reduces costs to 1/10 of the original search framework on average while maintaining effectiveness.

Large language models show promise for financial decision-making, yet deploying them as autonomous trading agents raises fundamental challenges: how to adapt instructions when rewards arrive late and obscured by market noise, how to synthesize heterogeneous information streams into coherent decisions, and how to bridge the gap between model outputs and executable market actions. We present ATLAS (Adaptive Trading with LLM AgentS), a unified multi-agent framework that integrates structured information from markets, news, and corporate fundamentals to support robust trading decisions. Within ATLAS, the central trading agent operates in an order-aware action space, ensuring that outputs correspond to executable market orders rather than abstract signals. The agent can incorporate feedback while trading using Adaptive-OPRO, a novel prompt-optimization technique that dynamically adapts the prompt by incorporating real-time, stochastic feedback, leading to increasing performance over time. Across regime-specific equity studies and multiple LLM families, Adaptive-OPRO consistently outperforms fixed prompts, while reflection-based feedback fails to provide systematic gains.

Recently, reward-conditioned reinforcement learning (RCRL) has gained popularity due to its simplicity, flexibility, and off-policy nature. However, we will show that current RCRL approaches are fundamentally limited and fail to address two critical challenges of RCRL -- improving generalization on high reward-to-go (RTG) inputs, and avoiding out-of-distribution (OOD) RTG queries during testing time. To address these challenges when training vanilla RCRL architectures, we propose Bayesian Reparameterized RCRL (BR-RCRL), a novel set of inductive biases for RCRL inspired by Bayes' theorem. BR-RCRL removes a core obstacle preventing vanilla RCRL from generalizing on high RTG inputs -- a tendency that the model treats different RTG inputs as independent values, which we term ``RTG Independence". BR-RCRL also allows us to design an accompanying adaptive inference method, which maximizes total returns while avoiding OOD queries that yield unpredictable behaviors in vanilla RCRL methods. We show that BR-RCRL achieves state-of-the-art performance on the Gym-Mujoco and Atari offline RL benchmarks, improving upon vanilla RCRL by up to 11%.

Future- or return-conditioned supervised learning is an emerging paradigm for offline reinforcement learning (RL), where the future outcome (i.e., return) associated with an observed action sequence is used as input to a policy trained to imitate those same actions. While return-conditioning is at the heart of popular algorithms such as decision transformer (DT), these methods tend to perform poorly in highly stochastic environments, where an occasional high return can arise from randomness in the environment rather than the actions themselves. Such situations can lead to a learned policy that is inconsistent with its conditioning inputs; i.e., using the policy to act in the environment, when conditioning on a specific desired return, leads to a distribution of real returns that is wildly different than desired. In this work, we propose the dichotomy of control (DoC), a future-conditioned supervised learning framework that separates mechanisms within a policy's control (actions) from those beyond a policy's control (environment stochasticity). We achieve this separation by conditioning the policy on a latent variable representation of the future, and designing a mutual information constraint that removes any information from the latent variable associated with randomness in the environment. Theoretically, we show that DoC yields policies that are consistent with their conditioning inputs, ensuring that conditioning a learned policy on a desired high-return future outcome will correctly induce high-return behavior. Empirically, we show that DoC is able to achieve significantly better performance than DT on environments that have highly stochastic rewards and transition

Building agents based on tree-search planning capabilities with learned models has achieved remarkable success in classic decision-making problems, such as Go and Atari. However, it has been deemed challenging or even infeasible to extend Monte Carlo Tree Search (MCTS) based algorithms to diverse real-world applications, especially when these environments involve complex action spaces and significant simulation costs, or inherent stochasticity. In this work, we introduce LightZero, the first unified benchmark for deploying MCTS/MuZero in general sequential decision scenarios. Specificially, we summarize the most critical challenges in designing a general MCTS-style decision-making solver, then decompose the tightly-coupled algorithm and system design of tree-search RL methods into distinct sub-modules. By incorporating more appropriate exploration and optimization strategies, we can significantly enhance these sub-modules and construct powerful LightZero agents to tackle tasks across a wide range of domains, such as board games, Atari, MuJoCo, MiniGrid and GoBigger. Detailed benchmark results reveal the significant potential of such methods in building scalable and efficient decision intelligence. The code is available as part of OpenDILab at https://github.com/opendilab/LightZero.

Mehta and Panigrahi (2012) proposed Online Matching with Stochastic Rewards, which generalizes the Online Bipartite Matching problem of Karp, Vazirani, and Vazirani (1990) by associating the edges with success probabilities. This new feature captures the pay-per-click model in online advertising. Recently, Huang and Zhang (2020) studied this problem under the online primal dual framework using the Configuration Linear Program (LP), and got the best known competitive ratios of the Stochastic Balance algorithm. Their work suggests that the more expressive Configuration LP is more suitable for this problem than the Matching LP. This paper advances the theory of Configuration LP in two directions. Our technical contribution includes a characterization of the joint matching outcome of an offline vertex and all its neighbors. This characterization may be of independent interest, and is aligned with the spirit of Configuration LP. By contrast, previous analyses of Ranking generally focus on only one neighbor. Second, we designed a Stochastic Configuration LP that captures a stochastic benchmark proposed by Goyal and Udwani (2020), who used a Path-based LP. The Stochastic Configuration LP is smaller and simpler than the Path-based LP. Moreover, using the new LP we improved the competitive ratio of Stochastic Balance from 0.596 to 0.611 when the success probabilities are infinitesimal, and to 0.613 when the success probabilities are further equal.

In the post-pandemic world, manufacturing enterprises face increasing uncertainties, especially with vulnerabilities in global supply chains. Although supply chain management has been extensively studied, the critical influence of decision-makers (DMs) in these systems remains underexplored. This study studies the inventory management problem under risk using the newsvendor model by incorporating DMs risk preferences. By employing the Quantum Monte Carlo (QMC) combined with Quantum Amplitude Estimation (QAE) algorithm, the estimation of probabilities or expectation values can be done more efficiently. This offers near-quadratic speedup compared to classical Monte Carlo methods. Our findings illuminate the intricate relationship between risk-aware decision-making and inventory management, providing essential insights for enhancing supply chain resilience and adaptability in uncertain conditions

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools, such as search engines and code interpreters, to solve tasks beyond the capabilities of language-only reasoning. While reinforcement learning (RL) has shown promise in improving TIR by optimizing final answer correctness, existing approaches often overlook the efficiency and cost associated with tool usage. This can lead to suboptimal behavior, including excessive tool calls that increase computational and financial overhead, or insufficient tool use that compromises answer quality. In this work, we propose Optimal Tool Call-controlled Policy Optimization (OTC-PO), a simple yet effective RL-based framework that encourages models to produce accurate answers with minimal tool calls. Our method introduces a tool-integrated reward that jointly considers correctness and tool efficiency, promoting high tool productivity. We instantiate this framework within both Proximal Policy Optimization (PPO) and Group Relative Preference Optimization (GRPO), resulting in OTC-PPO and OTC-GRPO. Experiments with Qwen-2.5 and Qwen-Math across multiple QA benchmarks show that our approach reduces tool calls by up to 73.1\% and improves tool productivity by up to 229.4\%, while maintaining comparable answer accuracy. To the best of our knowledge, this is the first RL-based framework that explicitly optimizes tool-use efficiency in TIR.

In this paper we develop a dynamic form of Bayesian optimization for machine learning models with the goal of rapidly finding good hyperparameter settings. Our method uses the partial information gained during the training of a machine learning model in order to decide whether to pause training and start a new model, or resume the training of a previously-considered model. We specifically tailor our method to machine learning problems by developing a novel positive-definite covariance kernel to capture a variety of training curves. Furthermore, we develop a Gaussian process prior that scales gracefully with additional temporal observations. Finally, we provide an information-theoretic framework to automate the decision process. Experiments on several common machine learning models show that our approach is extremely effective in practice.