Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning

Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios often feature inherent heterogeneity. Furthermore, most works on MFG assume access to a known MFG model, which might not be readily available for real-world finite-agent games. In this work, we broaden the applicability of MFGs by providing a methodology to extend any finite-player, possibly asymmetric, game to an "induced MFG". First, we prove that N-player dynamic games can be symmetrized and smoothly extended to the infinite-player continuum via explicit Kirszbraun extensions. Next, we propose the notion of, -symmetric games, a new class of dynamic population games that incorporate approximate permutation invariance. For, -symmetric games, we establish explicit approximation bounds, demonstrating that a Nash policy of the induced MFG is an approximate Nash of the N-player dynamic game. We show that TD learning converges up to a small bias using trajectories of the N-player game with finite-sample guarantees, permitting symmetrized learning without building an explicit MFG model. Finally, for certain games satisfying monotonicity, we prove a sample complexity of O (^-6) for the N-agent game to learn an -Nash up to symmetrization bias. Our theory is supported by evaluations on MARL benchmarks with thousands of agents.