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 $\Tilde{O}(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $\Tilde{O}(T^{-3/4})$ 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 $\Tilde{O}(T^{-1})$ convergence rate for computing a correlated equilibrium. Our algorithm is constructed by combining two main elements (i) smooth value updates and (ii) the \emph{optimistic-follow-the-regularized-leader} algorithm with the log barrier regularizer.