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Asuman Ozdaglar

Publications and source records attributed to Asuman Ozdaglar.

At least 19 recordsLinked to original sources
arXiv2026

Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion

Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

cs.LG↗
arXiv2026

Constant Individual Regret in General Games

Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite $N$-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If $m_{\max}$ denotes the largest action-set size, then, simultaneously for every horizon $T\geq1$, it guarantees that each of the $N$ players in the game incurs regret upper bounded by $O(\textrm{poly}(N, \log m_{\max}))$. Our algorithm leverages a new form of optimism inspired by modern filter design.

cs.LG↗
arXiv2026

Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex

We revisit the regret loss framework introduced in Park et al. (2025), which uses decision-theoretic regret as a direct loss function for training models to make better decisions, through the lens of probability-simplex policies. Our first result shows that a single-layer self-attention model trained with regret loss admits a stationary point whose forward-pass exactly matches smoothed fictitious play with the appropriate stepsize that ensures no-regret behavior-i.e., for any given policy input, the model outputs the same update that smoothed fictitious play would produce. In parallel, we also newly introduce a swap-regret loss function, which extends the regret-loss framework beyond external regret and enables models to directly optimize for swap-deviation robustness. We further show that this swap-regret loss admits a stationary point whose forward pass implements the corresponding swap-regret update induced by classical Blum-Mansour no-pass implementation algorithm, with each head implementing an external-regret update via smoothed fictitious play. Together, these results show that regret-trained attention can realize differentiable mechanisms whose deployment induces equilibrium behavior in games: external-regret dynamics lead to coarse correlated equilibrium, while swap-regret dynamics lead to correlated equilibrium. Thus, regret-based objectives steer minimal attention architectures toward online-learning dynamics with game-theoretic guarantees, without supervised traces of those algorithms.

cs.LG↗
arXiv2026

Training and Evaluating Diffusion Policies with Long Context Lengths

Imitation learning has enabled highly-dexterous robotic manipulation from RGB observations. Policies trained with these methods, however, typically condition robot actions on only a short history of observations. These policies cannot solve tasks that require memory and can get stuck repeatedly executing the same failing motions. In this work, we first benchmark policy performance as context length is incrementally increased from short to long, across a spectrum of tasks with varying local stability and memory requirements, and in multiple data regimes. To our knowledge, this is the first study to investigate context length for Diffusion Policies at this level of detail. Our results challenge prior claims: naively scaling context length is not as brittle as advertised in literature. With an appropriate conditioning method and denoising backbone (UNet+Cross-Attention), single-task policies achieve high success rates on many tasks in the usual data regime even with naive scaling. Next, we propose a training algorithm to jointly train policies at multiple context lengths, further reducing the sample complexity of long-context learning. Finally, we apply our findings to re-evaluate some previously proposed solutions to long-context imitation learning.

cs.RO↗
arXiv2026

Decentralized Best-Response-Based Learning in Two-Player Zero-Sum Stochastic Games: A Finite-Sample Analysis

We present a finite-sample analysis of decentralized learning in two-player zero-sum matrix games and stochastic games, with a focus on best-response-based learning algorithms. In matrix games, the learning algorithm is payoff-based and symmetric: each player updates its policy using only its own payoff observations, incrementally moving toward an estimated smoothed best response to the opponent's latest policy. For stochastic games, we build on this matrix-game primitive to develop a learning algorithm called value iteration with smoothed best response (VI-SBR), which combines smoothed-best-response learning in induced matrix games with a decentralized, model-free approximation of minimax value iteration. We establish finite-sample guarantees in both settings. For matrix games, our results imply a sample complexity of $\mathcal{O}(ε^{-1})$ for finding an $ε$-Nash distribution and, with explicit exploration, $\tilde{\mathcal{O}}(ε^{-8})$ for finding an $ε$-Nash equilibrium. For stochastic games, we prove that the exploration-enhanced VI-SBR algorithm achieves a sample complexity of $\tilde{\mathcal{O}}(ε^{-8})$ for finding an $ε$-Nash equilibrium. Technically, our analysis develops a coupled Lyapunov-drift framework. This framework simultaneously handles stochastic iterative algorithms with multiple interacting stochastic iterates, the non-zero-sum auxiliary games generated by independently updated value functions, and the time-inhomogeneous Markovian noise induced by time-varying policies. The resulting tools may be useful more broadly for analyzing learning algorithms with coupled stochastic iterates and nonstationary sampling processes.

cs.LG↗
arXiv2026

Equilibrium with Internal Transfers

Nash equilibrium (NE) arises from selfish utility maximization, yet its social welfare can be arbitrarily far from optimal. Moreover, computing an NE is intractable in general. We study augmented game models in which players use budget-balanced internal transfers to improve incentives before play. We first introduce \emph{Self-Enforcing Transfer Equilibrium} (SETE), where players commit to nonnegative peer-to-peer transfers that are paid only if the recipient does not deviate from a prescribed strategy. For polymatrix games, we show that every stationary point of the social welfare function, in particular any socially optimal strategy profile, can be sustained as a SETE. This induces a Nash equilibrium in the agent normal form of the corresponding augmented game. We further propose a polynomial-time algorithm and a decentralized learning dynamic to compute such product-form equilibria. We then introduce \emph{Mediated Self-Enforcing Transfer Equilibrium} (M-SETE), where a mediator makes both the payment schedule and the prescribed strategies binding offers. This additional enforcement resolves the agent-normal-form limitation: an M-SETE is a Nash equilibrium of the augmented game itself, not merely of its agent normal form, and any socially optimal strategy profile can be supported as an M-SETE in any finite game while preserving budget balance. Thus, internal transfers improve welfare and computation while preserving independent play on the equilibrium path. When full sequential-game stability is required, binding mediation provides the corresponding implementation.

cs.GT↗
arXiv2026

Spectral Scaling Laws of Muon

Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the orthonormalization with the Newton--Schulz (NS) iteration. Since NS is only approximate, directions with small singular values fail to be orthonormalized. In Muon, NS is applied to the momentum matrix at every step, yet little is known about how the singular value spectrum of these momentum matrices behaves during training, or how that behavior changes with model size. We present the first systematic study of this question. Tracking singular value quantiles of the momentum buffer across layers in models ranging from 77M to 2.8B parameters, we observe a consistent picture: after a short burn-in, the quantiles stabilize at a value determined by the layer type and model size. These stabilization values follow remarkably clean power laws in model size, with layer-dependent exponents. Layers up to mid-late depth scale very mildly with model size $M$ (around $M^{-0.25}$), so the standard 5-step NS configuration used at academic scale will continue to orthonormalize them at much larger scales. Some of the late layers, however, scale much more aggressively (up to $M^{-0.96}$) and will fall into the NS failure regime at frontier scale unless one uses more NS iterations or better-tuned coefficients. NS iterations are computationally expensive at scale; our laws give practitioners a principled, layer-aware recipe for choosing the minimum NS configuration that still orthonormalizes the directions that matter -- avoiding unnecessary computation without sacrificing update quality.

cs.LG↗
arXiv2026

Regret Minimization with Adaptive Opponents in Repeated Games

In this paper, we study regret minimization in repeated games with \emph{adaptive} opponents who can respond based on histories of play. The standard metric of \emph{external regret} in online learning is known to fail to capture such adaptivity. To account for players' counterfactual reasoning, we introduce {\tt Repeated Policy Regret (RP-Regret)}, a game-theoretic metric that measures the difference between the \emph{realized} and the \emph{best-in-hindsight} accumulated utility when all players can \emph{respond} to the history of play. Compared to existing regret notions in this setting, ours is native to repeated game playing, enabling stronger comparators and opponents with fewer constraints, while maintaining the possibility of finding better equilibria when all players minimize it. We first identify necessary conditions for obtaining {\tt RP-Regret} sublinear in time, on the variation of the player's comparator strategies in the regret definition and on the memories of both the comparator and opponents' strategies. We then study additional conditions and provable algorithms to minimize {\tt RP-Regret}, which is by definition \emph{non-convex} in the strategy space. To address this challenge, we propose three algorithms: (i) one based on an optimization oracle, as assumed in some prior work in online non-convex learning; (ii) one that minimizes a convex and \emph{linearized} surrogate of {\tt RP-Regret} at each iteration; (iii) one that directly minimizes {\tt RP-Regret} when opponents change strategies slowly. Furthermore, when all players can run algorithms to minimize the {\tt RP-Regret} (or its linearized variant), certain subgame perfect equilibria of the repeated game can be learned. We also provide experiments showing that minimizing our regret notions can lead to more cooperative solutions with higher utility in games such as Stag-Hunt.

cs.LG↗
arXiv2026

AI Behavioral Science

We outline a foundation for a new field of ``AI Behavioral Science,'' covering three perspectives. First, as AI becomes ubiquitous and is increasingly proprietary and opaque, it becomes vital to develop techniques for assessing AI behavior. We outline how tools developed to assess people's behaviors by social scientists can be used to assess and infer AI's behaviors biases, tendencies, and heuristics. Second, we also discuss how AI can change the ways in which we learn about human behavior. Beyond its computational power, AI offers new techniques for simulating, inferring, and predicting human behaviors that we outline and discuss. Third, as humans and AI are interacting in increasingly complex and intertwined systems, we need to understand the implications for the resulting economic and political outcomes. We outline issues that are increasingly pressing concerning the future of human-AI interactions and potential changes and disruptions that can ensue.

cs.HC↗
arXiv2026

Post-Training LLMs as Better Decision-Making Agents: A Regret-Minimization Approach

Large language models (LLMs) are increasingly deployed as "agents" for decision-making (DM) in interactive and dynamic environments. Yet, since they were not originally designed for DM, recent studies show that LLMs can struggle even in basic online DM problems, failing to achieve low regret or an effective exploration-exploitation tradeoff. To address this, we introduce Iterative Regret-Minimization Fine-Tuning (Iterative RMFT), a post-training procedure that repeatedly distills low-regret decision trajectories back into the base model. At each iteration, the model rolls out multiple decision trajectories, selects the k-lowest regret ones, and fine-tunes itself on them. Unlike prior methods that (a) distill action sequences from known DM algorithms or (b) rely on manually crafted chain-of-thought templates, our approach leverages the regret metric to elicit the model's own DM ability and reasoning rationales. This reliance on model-generated reasoning avoids rigid output engineering and provides more flexible, natural-language training signals. Empirical results show that Iterative RMFT improves LLMs' DM performance across diverse models - from Transformers with numerical input/output, to open-weight LLMs, and advanced closed-weight models like GPT-4o mini. Its flexibility in output and reasoning formats enables generalization across tasks with varying horizons, action spaces, reward processes, and natural-language contexts. Finally, we provide theoretical insight showing that a single-layer Transformer under this paradigm can act as a no-regret learner in a simplified setting. Overall, Iterative RMFT offers a principled and general post-training framework for enhancing LLMs' decision-making capabilities.

cs.AI↗
arXiv2026

Collaborative and Efficient Fine-tuning: Leveraging Task Similarity

Adaptability has been regarded as a central feature in the foundation models, enabling them to effectively acclimate to unseen downstream tasks. Parameter-efficient fine-tuning methods such as celebrated LoRA facilitate efficient adaptation of large foundation models using labeled, high-quality and generally scarce task data. To mitigate data scarcity in fine-tuning of foundation models, we propose to leverage task similarity across multiple downstream users. Intuitively, users with similar tasks must be able to assist each other in boosting the effective fine-tuning data size. We propose Collaborative Low-Rank Adaptation, or CoLoRA, which exploits task similarity to collaboratively and efficiently fine-tune personalized foundation models. The main idea in CoLoRA is to train one shared adapter capturing underlying task similarities across all tasks, and personalized adapters tailored to user-specific tasks. We theoretically study CoLoRA on heterogeneous linear regression and provide provable guarantees for ground truth recovery. We also conduct several natural language experiments with varying task similarity, which further demonstrate that when trained together with similar tasks, individual performances are significantly boosted.

cs.LG↗
arXiv2026

Learning Decision-Sufficient Representations for Linear Optimization

We study how to construct compressed datasets that suffice to recover optimal decisions in linear programs with an unknown cost vector $c$ lying in a prior set $\mathcal{C}$. Recent work by Bennouna et al. provides an exact geometric characterization of sufficient decision datasets (SDDs) via an intrinsic decision-relevant dimension $d^\star$. However, their algorithm for constructing minimum-size SDDs requires solving mixed-integer programs. In this paper, we establish hardness results showing that computing $d^\star$ is NP-hard and deciding whether a dataset is globally sufficient is coNP-hard, thereby resolving a recent open problem posed by Bennouna et al. To address this worst-case intractability, we introduce pointwise sufficiency, a relaxation that requires sufficiency for an individual cost vector. Under nondegeneracy, we provide a polynomial-time cutting-plane algorithm for constructing pointwise-sufficient decision datasets. In a data-driven regime with i.i.d.\ costs, we further propose a cumulative algorithm that aggregates decision-relevant directions across samples, yielding a stable compression scheme of size at most $d^\star$. This leads to a distribution-free PAC guarantee: with high probability over the training sample, the pointwise sufficiency failure probability on a fresh draw is at most $\tilde{O}(d^\star/n)$, and this rate is tight up to logarithmic factors. Finally, we apply decision-sufficient representations to contextual linear optimization, obtaining compressed predictors with generalization bounds scaling as $\tilde{O}(\sqrt{d^\star/n})$ rather than $\tilde{O}(\sqrt{d/n})$, where $d$ is the ambient cost dimension.

math.OC↗
arXiv2026

Computing Equilibrium beyond Unilateral Deviation

Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes solution concepts that provide stability against multilateral deviations (\emph{e.g.}, strong Nash and coalition-proof equilibrium), these generally fail to exist. In this paper, we study an alternative solution concept that minimizes coalitional deviation incentives, rather than requiring them to vanish, and is therefore guaranteed to exist. Specifically, we focus on minimizing the average gain of a deviating coalition, and extend the framework to weighted-average and maximum-within-coalition gains. In contrast, the minimum-gain analogue is shown to be computationally intractable. For the average-gain and maximum-gain objectives, we prove a lower bound on the complexity of computing such an equilibrium and present an algorithm that matches this bound. Finally, we use our framework to solve the \emph{Exploitability Welfare Frontier} (EWF), the maximum attainable social welfare subject to a given exploitability (the maximum gain over all unilateral deviations).

cs.GT↗
arXiv2026

How AI Aggregation Affects Knowledge

Artificial intelligence (AI) changes social learning when aggregated outputs become training data for future predictions. To study this, we extend the DeGroot model by introducing an AI aggregator that trains on population beliefs and feeds synthesized signals back to agents. We define the learning gap as the deviation of long-run beliefs from the efficient benchmark, allowing us to capture how AI aggregation affects learning. Our main result identifies a threshold in the speed of updating: when the aggregator updates too quickly, there is no positive-measure set of training weights that robustly improves learning across a broad class of environments, whereas such weights exist when updating is sufficiently slow. We then compare global and local architectures. Local aggregators trained on proximate or topic-specific data robustly improve learning in all environments. Consequently, replacing specialized local aggregators with a single global aggregator worsens learning in at least one dimension of the state.

econ.TH↗
arXiv2026

Online Learning and Equilibrium Computation with Ranking Feedback

Online learning in arbitrary, and possibly adversarial, environments has been extensively studied in sequential decision-making, and it is closely connected to equilibrium computation in game theory. Most existing online learning algorithms rely on \emph{numeric} utility feedback from the environment, which may be unavailable in human-in-the-loop applications and/or may be restricted by privacy concerns. In this paper, we study an online learning model in which the learner only observes a \emph{ranking} over a set of proposed actions at each timestep. We consider two ranking mechanisms: rankings induced by the \emph{instantaneous} utility at the current timestep, and rankings induced by the \emph{time-average} utility up to the current timestep, under both \emph{full-information} and \emph{bandit} feedback settings. Using the standard external-regret metric, we show that sublinear regret is impossible with instantaneous-utility ranking feedback in general. Moreover, when the ranking model is relatively deterministic, \emph{i.e.}, under the Plackett-Luce model with a temperature that is sufficiently small, sublinear regret is also impossible with time-average utility ranking feedback. We then develop new algorithms that achieve sublinear regret under the additional assumption that the utility sequence has sublinear total variation. Notably, for full-information time-average utility ranking feedback, this additional assumption can be removed. As a consequence, when all players in a normal-form game follow our algorithms, repeated play yields an approximate coarse correlated equilibrium. We also demonstrate the effectiveness of our algorithms in an online large-language-model routing task.

cs.LG↗
arXiv2026

Differentially Private Equilibrium Finding in Polymatrix Games

We study equilibrium finding in polymatrix games under differential privacy constraints. Prior work in this area fails to achieve both high-accuracy equilibria and a low privacy budget. To better understand the fundamental limitations of differential privacy in games, we show hardness results establishing that no algorithm can simultaneously obtain high accuracy and a vanishing privacy budget as the number of players tends to infinity. This impossibility holds in two regimes: (i) We seek to establish equilibrium approximation guarantees in terms of Euclidean \emph{distance} to the equilibrium set, and (ii) The adversary has access to all communication channels. We then consider the more realistic setting in which the adversary can access only a bounded number of channels and propose a new distributed algorithm that: recovers strategies with simultaneously vanishing \emph{Nash gap} (in expected utility, also referred to as \emph{exploitability}) and \emph{privacy budget} as the number of players increases. Our approach leverages structural properties of polymatrix games. To our knowledge, this is the first paper that can achieve this in equilibrium computation. Finally, we also provide numerical results to justify our algorithm.

cs.GT↗
arXiv2026

Beyond RLHF and NLHF: Population-Proportional Alignment under an Axiomatic Framework

Conventional preference learning methods often prioritize opinions held more widely when aggregating preferences from multiple evaluators. This may result in policies that are biased in favor of some types of opinions or groups and susceptible to strategic manipulation. To address this issue, we develop a novel preference learning framework capable of aligning aggregate opinions and policies proportionally with the true population distribution of evaluator preferences. Grounded in social choice theory, our approach infers the feasible set of evaluator population distributions directly from pairwise comparison data. Using these estimates, the algorithm constructs a policy that satisfies foundational axioms from social choice theory, namely monotonicity and Pareto efficiency, as well as our newly-introduced axioms of population-proportional alignment and population-bounded manipulability. Moreover, we propose a soft-max relaxation method that smoothly trades off population-proportional alignment with the selection of the Condorcet winner (which beats all other options in pairwise comparisons). Finally, we validate the effectiveness and scalability of our approach through experiments on both tabular recommendation tasks and large language model alignment.

cs.AI↗
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↗