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˜O(T−1) Convergence to (coarse) correlated equilibria in full-information general-sum Markov games
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:361-374, 2024.
Abstract
No-regret learning has a long history of being closely connected to game theory. Recent works have devised uncoupled no-regret learning dynamics that, when adopted by all the players in normal-form games, converge to various equilibrium solutions at a near-optimal rate of ˜O(T−1), a significant improvement over the O(1/√T) rate of classic no-regret learners. However, analogous convergence results are scarce in Markov games, a more generic setting that lays the foundation for multi-agent reinforcement learning. In this work, we close this gap by showing that the optimistic-follow-the-regularized-leader (OFTRL) algorithm, together with appropriate value update procedures, can find ˜O(T−1)-approximate (coarse) correlated equilibria in full-information general-sum Markov games within T iterations. Numerical results are also included to corroborate our theoretical findings.