Near-Optimal Policy Optimization for Correlated Equilibrium in General-Sum Markov Games

We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve O(T^-1/2) convergence rate to a correlated equilibrium and an accelerated O(T^-3/4) convergence rate to the weaker notion of coarse correlated equilibrium. In this paper, we improve both results significantly by providing an uncoupled policy optimization algorithm that attains a near-optimal Õ(T^-1) convergence rate for computing a correlated equilibrium. Our algorithm is constructed by combining two main elements (i) smooth value updates and (ii) the optimistic-follow-the-regularized-leader algorithm with the log barrier regularizer.