Interactive Distributionally Robust Multi-Agent Learning with General Function Approximation

Debamita Ghosh, George K. Atia, Yue Wang

Model misspecification poses a fundamental challenge in multi-agent reinforcement learning, where transition uncertainty can be amplified by strategic interactions among agents. Distributionally robust Markov games (DRMGs) provide a principled framework for addressing such uncertainty, yet existing methods often rely on restrictive assumptions or scale poorly to large state and joint action spaces. We study online learning in general-sum DRMGs with general function approximation and $φ$-divergence uncertainty sets. We propose RoMEX-$φ$, a model-free framework that integrates equilibrium-based exploration with dual fitted learning. Through a functional dual representation of the robust multi-agent Bellman operator, RoMEX-$φ$ enables tractable worst-case value estimation from nominal interaction data using a centered empirical robust discrepancy. We introduce the robust Multi-Agent Decoupling Coefficient (robust MADC) to characterize the intrinsic exploration complexity arising from strategic interactions and adversarial transition uncertainty. We establish sublinear robust regret guarantees governed by the robust MADC rather than explicitly by the state and joint action space…