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

We study policy optimization algorithms for computing correlated equilibria in multiplayer general-sum Markov Games. Previous results achieve (O) over tilde (T-1/2) convergence rate to a correlated equilibrium and an accelerated (O) over tilde (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 (O) over tilde (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 optimisticfollow-the-regularized-leader algorithm with the log barrier regularizer.