arXiv subjects

Asuman Ozdaglar

Publications and source records attributed to Asuman Ozdaglar.

At least 37 records · Page 2Linked to original sources

arXiv2026

Data Informativeness in Linear Optimization under Uncertainty

We study the problem of determining what data is required to solve a decision-making task when only partial information about the state of the world is available. Focusing on linear programs, we introduce a decision-focused notion of data informativeness that formalizes when a data set is sufficient to recover the optimal decision. Our notion abstracts away the notion of estimators (how data is used): it depends solely on the structure of the optimization task and the uncertainty. Our main result provides a geometric characterization of data sufficiency: a data set is sufficient if and only if, together with prior knowledge, it captures all cost directions that can change the optimal solution, given the task structure and the uncertainty set. Building on our characterization, we develop a tractable algorithm to determine minimal sufficient data sets under general data collection constraints. Taken together, our work introduces a principled framework for task-aware data collection. We demonstrate the approach in two applications: selecting where to conduct field experiments to inform infrastructure design and choosing which candidates to interview in order to make an optimal hiring decision. Our results illustrate that small, carefully selected data sets often suffice to determine the optimal decisions.

math.OC↗

arXiv2026

A Bayesian Framework for Human-AI Collaboration: Complementarity and Correlation Neglect

We develop a decision-theoretic model of human-AI interaction to study when AI assistance improves or impairs human decision-making. A human decision-maker observes private information and receives a recommendation from an AI system, but may combine these signals imperfectly. We show that the effect of AI assistance decomposes into two main forces: the marginal informational value of the AI beyond what the human already knows, and a behavioral distortion arising from how the human uses the AI's recommendation. Central to our analysis is a micro-founded measure of informational overlap between human and AI knowledge. We study an empirically relevant form of imperfect decision-making -- correlation neglect -- whereby humans treat AI recommendations as independent of their own information despite shared evidence. Under this model, we characterize how overlap and AI capabilities shape the Human-AI interaction regime between augmentation, impairment, complementarity, and automation, and draw key insights.

cs.GT↗

arXiv2026

Equilibrium Selection for Multi-agent Reinforcement Learning: A Unified Framework

While multi-agent reinforcement learning (MARL) has produced numerous algorithms that converge to Nash or related equilibria, such equilibria are often non-unique and can exhibit widely varying efficiency. This raises a fundamental question: how can one design learning dynamics that not only converge to equilibrium but also select equilibria with desirable performance, such as high social welfare? In contrast to the MARL literature, equilibrium selection has been extensively studied in normal-form games, where decentralized dynamics are known to converge to potential-maximizing or Pareto-optimal Nash equilibria (NEs). Motivated by these results, we study equilibrium selection in finite-horizon stochastic games. We propose a unified actor-critic framework in which a critic learns state-action value functions, and an actor applies a classical equilibrium-selection rule state-wise, treating learned values as stage-game payoffs. We show that, under standard stochastic stability assumptions, the stochastically stable policies of the resulting dynamics inherit the equilibrium selection properties of the underlying normal-form learning rule. As consequences, we obtain potential-maximizing policies in Markov potential games and Pareto-optimal (Markov perfect) equilibria in general-sum stochastic games, together with sample-based implementation of the framework.

cs.GT↗

arXiv2026

Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization

Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or restrict attention to convex settings, leaving nonconvex optimization with black-box constraints largely unexplored. We propose the zeroth-order feedback-linearization (ZOFL) algorithm for ZO constrained optimization that enforces feasibility without access to the first-order oracle of the constraint functions and applies to both equality and inequality constraints. The proposed approach relies only on noisy, sample-based gradient estimates obtained via two-point estimators, yet provably guarantees constraint satisfaction under mild regularity conditions. It adopts a control-theoretic perspective on ZO constrained optimization and leverages feedback linearization, a nonlinear control technique, to enforce feasibility. Finite-time bounds on constraint violation and asymptotic global convergence guarantees are established for the ZOFL algorithm. A midpoint discretization variant is further developed to improve feasibility without sacrificing optimality. Empirical results demonstrate that ZOFL consistently outperforms standard ZO baselines, achieving competitive objective values while maintaining feasibility.

math.OC↗

arXiv2025

Optimism as Risk-Seeking in Multi-Agent Reinforcement Learning

Risk sensitivity has become a central theme in reinforcement learning (RL), where convex risk measures and robust formulations provide principled ways to model preferences beyond expected return. Recent extensions to multi-agent RL (MARL) have largely emphasized the risk-averse setting, prioritizing robustness to uncertainty. In cooperative MARL, however, such conservatism often leads to suboptimal equilibria, and a parallel line of work has shown that optimism can promote cooperation. Existing optimistic methods, though effective in practice, are typically heuristic and lack theoretical grounding. Building on the dual representation for convex risk measures, we propose a principled framework that interprets risk-seeking objectives as optimism. We introduce optimistic value functions, which formalize optimism as divergence-penalized risk-seeking evaluations. Building on this foundation, we derive a policy-gradient theorem for optimistic value functions, including explicit formulas for the entropic risk/KL-penalty setting, and develop decentralized optimistic actor-critic algorithms that implement these updates. Empirical results on cooperative benchmarks demonstrate that risk-seeking optimism consistently improves coordination over both risk-neutral baselines and heuristic optimistic methods. Our framework thus unifies risk-sensitive learning and optimism, offering a theoretically grounded and practically effective approach to cooperation in MARL.

cs.LG↗

arXiv2025

UFT: Unifying Supervised and Reinforcement Fine-Tuning

Post-training has demonstrated its importance in enhancing the reasoning capabilities of large language models (LLMs). The primary post-training methods can be categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). SFT is efficient and well-suited for small language models, but it may lead to overfitting and limit the reasoning abilities of larger models. In contrast, RFT generally yields better generalization but depends heavily on the strength of the base model. To address the limitations of SFT and RFT, we propose Unified Fine-Tuning (UFT), a novel post-training paradigm that unifies SFT and RFT into a single, integrated process. UFT enables the model to effectively explore solutions while incorporating informative supervision signals, bridging the gap between memorizing and thinking underlying existing methods. Notably, UFT outperforms both SFT and RFT in general, regardless of model sizes. Furthermore, we theoretically prove that UFT breaks RFT's inherent exponential sample complexity bottleneck, showing for the first time that unified training can exponentially accelerate convergence on long-horizon reasoning tasks.

cs.LG↗

arXiv2025

Do LLM Agents Have Regret? A Case Study in Online Learning and Games

Large language models (LLMs) have been increasingly employed for (interactive) decision-making, via the development of LLM-based autonomous agents. Despite their emerging successes, the performance of LLM agents in decision-making has not been fully investigated through quantitative metrics, especially in the multi-agent setting when they interact with each other, a typical scenario in real-world LLM-agent applications. To better understand the limits of LLM agents in these interactive environments, we propose to study their interactions in benchmark decision-making settings in online learning and game theory, through the performance metric of \emph{regret}. We first empirically study the {no-regret} behaviors of LLMs in canonical (non-stationary) online learning problems, as well as the emergence of equilibria when LLM agents interact through playing repeated games. We then provide some theoretical insights into the no-regret behaviors of LLM agents, under certain assumptions on the supervised pre-training and the rationality model of human decision-makers who generate the data. Notably, we also identify (simple) cases where advanced LLMs such as GPT-4 fail to be no-regret. To promote the no-regret behaviors, we propose a novel \emph{unsupervised} training loss of \emph{regret-loss}, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. We then establish the statistical guarantee of generalization bound for regret-loss minimization, followed by the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms. Our further experiments demonstrate the effectiveness of our regret-loss, especially in addressing the above ``regrettable'' cases.

cs.LG↗

arXiv2025

Optimal interventions in opinion dynamics on large-scale, time-varying, random networks

We consider two optimization problems in which a planner aims to influence the average transient opinion in the Friedkin-Johnsen dynamics on a network by intervening on the agents' innate opinions. Solving these problems requires full network knowledge, which is often not available because of the cost involved in collecting this information or due to privacy considerations. For this reason, we focus on intervention strategies that are based on statistical instead of exact knowledge of the network. We focus on a time-varying random network model where the network is resampled at each time step and formulate two intervention problems in this setting. We show that these problems can be casted into mixed integer linear programs in the type space, where the type of a node captures its out- and in-degree and other local features of the nodes, and provide a closed form solution for one of the two problems. The integer constraints may be easily removed using probabilistic interventions leading to linear programs. Finally, we show by a numerical analysis that there are cases in which the derived optimal interventions on time-varying networks can lead to close to optimal interventions on fixed networks.

physics.soc-ph↗

arXiv2025

Finite-Sample Guarantees for Learning Dynamics in Zero-Sum Polymatrix Games

We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The first setting is the full information case, in which each player knows their own and their opponents' payoff matrices and observes everyone's mixed strategies. The second setting is the minimal information case, where players do not observe their opponents' strategies and are not aware of any payoff matrices (instead they only observe their realized payoffs). For this setting, also known as the radically uncoupled case in the learning in games literature, we study a two-timescale learning dynamics that combine smoothed best-response type updates for strategy estimates with a TD-learning update to estimate a local payoff function. For these dynamics, without additional exploration, we provide polynomial-time finite-sample guarantees for convergence to an $ε$-Nash equilibrium.

math.OC↗

arXiv2025

Multi-Player Zero-Sum Markov Games with Networked Separable Interactions

We study a new class of Markov games, \emph(multi-player) zero-sum Markov Games} with \emph{Networked separable interactions} (zero-sum NMGs), to model the local interaction structure in non-cooperative multi-agent sequential decision-making. We define a zero-sum NMG as a model where {the payoffs of the auxiliary games associated with each state are zero-sum and} have some separable (i.e., polymatrix) structure across the neighbors over some interaction network. We first identify the necessary and sufficient conditions under which an MG can be presented as a zero-sum NMG, and show that the set of Markov coarse correlated equilibrium (CCE) collapses to the set of Markov Nash equilibrium (NE) in these games, in that the product of per-state marginalization of the former for all players yields the latter. Furthermore, we show that finding approximate Markov \emph{stationary} CCE in infinite-horizon discounted zero-sum NMGs is \texttt{PPAD}-hard, unless the underlying network has a ``star topology''. Then, we propose fictitious-play-type dynamics, the classical learning dynamics in normal-form games, for zero-sum NMGs, and establish convergence guarantees to Markov stationary NE under a star-shaped network structure. Finally, in light of the hardness result, we focus on computing a Markov \emph{non-stationary} NE and provide finite-iteration guarantees for a series of value-iteration-based algorithms. We also provide numerical experiments to corroborate our theoretical results.

cs.GT↗

arXiv2025

MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning

Leveraging multiple large language models (LLMs) to build collaborative multi-agentic workflows has demonstrated significant potential. However, most previous studies focus on prompting the out-of-the-box LLMs, relying on their innate capability for collaboration, which may not improve LLMs' performance as shown recently. In this paper, we introduce a new post-training paradigm MAPoRL (Multi-Agent Post-co-training for collaborative LLMs with Reinforcement Learning), to explicitly elicit the collaborative behaviors and further unleash the power of multi-agentic LLM frameworks. In MAPoRL, multiple LLMs first generate their own responses independently and engage in a multi-turn discussion to collaboratively improve the final answer. In the end, a MAPoRL verifier evaluates both the answer and the discussion, by assigning a score that verifies the correctness of the answer, while adding incentives to encourage corrective and persuasive discussions. The score serves as the co-training reward, and is then maximized through multi-agent RL. Unlike existing LLM post-training paradigms, MAPoRL advocates the co-training of multiple LLMs together using RL for better generalization. Accompanied by analytical insights, our experiments demonstrate that training individual LLMs alone is insufficient to induce effective collaboration. In contrast, multi-agent co-training can boost the collaboration performance across benchmarks, with generalization to unseen domains.

cs.AI↗

arXiv2025

The Power of Regularization in Solving Extensive-Form Games

In this paper, we investigate the power of {\it regularization}, a common technique in reinforcement learning and optimization, in solving extensive-form games (EFGs). We propose a series of new algorithms based on regularizing the payoff functions of the game, and establish a set of convergence results that strictly improve over the existing ones, with either weaker assumptions or stronger convergence guarantees. In particular, we first show that dilated optimistic mirror descent (DOMD), an efficient variant of OMD for solving EFGs, with adaptive regularization can achieve a fast $\tilde O(1/T)$ {last-iterate convergence rate for the output of the algorithm} in terms of duality gap and distance to the set of Nash equilibrium (NE) without uniqueness assumption of the NE. Second, we show that regularized counterfactual regret minimization (\texttt{Reg-CFR}), with a variant of optimistic mirror descent algorithm as regret-minimizer, can achieve $O(1/T^{1/4})$ best-iterate, and $O(1/T^{3/4})$ average-iterate convergence rate for finding NE in EFGs. Finally, we show that \texttt{Reg-CFR} can achieve asymptotic last-iterate convergence, and optimal $O(1/T)$ average-iterate convergence rate, for finding the NE of perturbed EFGs, which is useful for finding approximate extensive-form perfect equilibria (EFPE). To the best of our knowledge, they constitute the first last-iterate convergence results for CFR-type algorithms, while matching the state-of-the-art average-iterate convergence rate in finding NE for non-perturbed EFGs. We also provide numerical results to corroborate the advantages of our algorithms.

cs.GT↗

arXiv2025

A Policy-Gradient Approach to Solving Imperfect-Information Games with Best-Iterate Convergence

Policy gradient methods have become a staple of any single-agent reinforcement learning toolbox, due to their combination of desirable properties: iterate convergence, efficient use of stochastic trajectory feedback, and theoretically-sound avoidance of importance sampling corrections. In multi-agent imperfect-information settings (extensive-form games), however, it is still unknown whether the same desiderata can be guaranteed while retaining theoretical guarantees. Instead, sound methods for extensive-form games rely on approximating \emph{counterfactual} values (as opposed to Q values), which are incompatible with policy gradient methodologies. In this paper, we investigate whether policy gradient can be safely used in two-player zero-sum imperfect-information extensive-form games (EFGs). We establish positive results, showing for the first time that a policy gradient method leads to provable best-iterate convergence to a regularized Nash equilibrium in self-play.

cs.GT↗

arXiv2025

What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimization

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions -- offering a principled foundation for task-aware data selection.

math.OC↗

arXiv2025

Addressing misspecification in contextual optimization

We study a linear contextual optimization problem where a decision maker has access to historical data and contextual features to learn a cost prediction model aimed at minimizing decision error. We adopt the predict-then-optimize framework for this analysis. Given that perfect model alignment with reality is often unrealistic in practice, we focus on scenarios where the chosen hypothesis set is misspecified. In this context, it remains unclear whether current contextual optimization approaches can effectively address such model misspecification. In this paper, we present a novel integrated learning and optimization approach designed to tackle model misspecification in contextual optimization. This approach offers theoretical generalizability, tractability, and optimality guarantees, along with strong practical performance. Our method involves minimizing a tractable surrogate loss that aligns with the performance value from cost vector predictions, regardless of whether the model is misspecified, and can be optimized in reasonable time. To our knowledge, no previous work has provided an approach with such guarantees in the context of model misspecification.

math.OC↗

arXiv2025

Wikipedia Contributions in the Wake of ChatGPT

How has Wikipedia activity changed for articles with content similar to ChatGPT following its introduction? We estimate the impact using differences-in-differences models, with dissimilar Wikipedia articles as a baseline for comparison, to examine how changes in voluntary knowledge contributions and information-seeking behavior differ by article content. Our analysis reveals that newly created, popular articles whose content overlaps with ChatGPT 3.5 saw a greater decline in editing and viewership after the November 2022 launch of ChatGPT than dissimilar articles did. These findings indicate heterogeneous substitution effects, where users selectively engage less with existing platforms when AI provides comparable content. This points to potential uneven impacts on the future of human-driven online knowledge contributions.

cs.HC↗

arXiv2024

Offline Reinforcement Learning via Linear-Programming with Error-Bound Induced Constraints

Offline reinforcement learning (RL) aims to find an optimal policy for Markov decision processes (MDPs) using a pre-collected dataset. In this work, we revisit the linear programming (LP) reformulation of Markov decision processes for offline RL, with the goal of developing algorithms with optimal $O(1/\sqrt{n})$ sample complexity, where $n$ is the sample size, under partial data coverage and general function approximation, and with favorable computational tractability. To this end, we derive new \emph{error bounds} for both the dual and primal-dual formulations of the LP, and incorporate them properly as \emph{constraints} in the LP reformulation. We then show that under a completeness-type assumption, $O(1/\sqrt{n})$ sample complexity can be achieved under standard single-policy coverage assumption, when one properly \emph{relaxes} the occupancy validity constraint in the LP. This framework can readily handle both infinite-horizon discounted and average-reward MDPs, in both general function approximation and tabular cases. The instantiation to the tabular case achieves either state-of-the-art or the first sample complexities of offline RL in these settings. To further remove any completeness-type assumption, we then introduce a proper \emph{lower-bound constraint} in the LP, and a variant of the standard single-policy coverage assumption. Such an algorithm leads to a $O(1/\sqrt{n})$ sample complexity with dependence on the \emph{value-function gap}, with only realizability assumptions. Our properly constrained LP framework advances the existing results in several aspects, in relaxing certain assumptions and achieving the optimal $O(1/\sqrt{n})$ sample complexity, with simple analyses. We hope our results bring new insights into the use of LP formulations and the equivalent primal-dual minimax optimization for offline RL, through the error-bound induced constraints.

cs.LG↗

arXiv2024

A Unified Linear Programming Framework for Offline Reward Learning from Human Demonstrations and Feedback

Inverse Reinforcement Learning (IRL) and Reinforcement Learning from Human Feedback (RLHF) are pivotal methodologies in reward learning, which involve inferring and shaping the underlying reward function of sequential decision-making problems based on observed human demonstrations and feedback. Most prior work in reward learning has relied on prior knowledge or assumptions about decision or preference models, potentially leading to robustness issues. In response, this paper introduces a novel linear programming (LP) framework tailored for offline reward learning. Utilizing pre-collected trajectories without online exploration, this framework estimates a feasible reward set from the primal-dual optimality conditions of a suitably designed LP, and offers an optimality guarantee with provable sample efficiency. Our LP framework also enables aligning the reward functions with human feedback, such as pairwise trajectory comparison data, while maintaining computational tractability and sample efficiency. We demonstrate that our framework potentially achieves better performance compared to the conventional maximum likelihood estimation (MLE) approach through analytical examples and numerical experiments.

cs.LG↗