Distributionally Robust Markov Games with Average Reward

Deploying multi-agent reinforcement learning (MARL) in the real world is often limited by model mismatches between the training simulators and the true environment, which could be further amplified through strategic interactions and result in severe performance degradation upon deployment. Distributional robustness offers a principled response by optimizing policies against worst-case transition models drawn from an uncertainty set, but standard robust MARL frameworks become increasingly intractable as the number of agents grows. This paper develops an infinite-horizon, stationary mean-field game framework that incorporates distributional model uncertainty directly into the population-coupled dynamics. We establish a robust dynamic programming principle with a contractive Bellman operator and prove the existence of a stationary robust mean-field equilibrium via a fixed-point argument. We further develop the first concrete algorithm with convergence guarantees. We then connect the mean-field solution to a finite-population robust game whose ambiguity sets depend on the empirical distribution, showing that the mean-field equilibrium policy induces approximate equilibrium behavior as the population size increases. Under a contractive robust-dynamics regime, we further obtain explicit non-asymptotic error bounds. Numerical experiments further illustrate the qualitative and quantitative impact of robustness under multiple uncertainty models, validating our theoretical findings.

Multi-agent reinforcement learning (MARL) holds great potential but faces robustness challenges due to environmental uncertainty. To address this, distributionally robust Markov games (RMGs) optimize worst-case performance when the environment deviates from the nominal model within a uncertainty set. Beyond robustness, an equally urgent goal for MARL is data efficiency -- sampling from vast state and action spaces that grow exponentially with the number of agents potentially leads to the curse of multiagency. However, current provably data-efficient algorithms for RMGs are limited to tabular settings with finite state and action spaces, which are only computationally manageable for small-scale problems, leaving RMGs with large-scale (or infinite) state spaces largely unexplored. The only existing work beyond tabular settings focuses on linear function approximation (LFA) for a restrictive class of RMGs using vanish minimal value assumption and still suffers from sample complexity with the curse of multiagency. In this work, we focuses on general RMGs with LFA. For uncertainty sets defined by total variation distance, we develop provably data-efficient algorithms that break the curse of multiagency in both the generative model setting and a newly proposed online interactive setting. To our knowledge, our results are the first to break the curse of multiagency of sample complexity for RMGs with large (possibly infinite) state spaces, regardless of the uncertainty set construction.

We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs). We present non-asymptotic convergence analyses of Q-learning and actor-critic algorithms for robust average-reward MDPs under contamination, total-variation distance, and Wasserstein uncertainty sets. A key ingredient of our analysis is showing that the optimal robust Bellman operator is a strict contraction with respect to a carefully designed semi-norm. This property enables a stochastic approximation update that learns the optimal robust $Q$-function with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We also establish robust TD convergence bounds whose constants are uniform over all stationary policies, yielding an efficient data-driven routine for robust critic estimation. Building on this, we introduce an actor-critic algorithm that learns an $ε$-optimal robust policy with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We provide numerical simulations to illustrate the qualitative behavior of the proposed algorithms. Our results contribute to the theoretical foundations of robust planning under model misspecification and to model-free approaches for building robust long-run policies directly from simulation data.