Decentralized Robust V-Learning for Solving Markov Games with Model Uncertainty

Abstract

The Markov game is a popular reinforcement learning framework for modeling competitive players in a dynamic environment. However, most of the existing works on Markov games focus on computing a certain equilibrium following uncertain interactions among the players but ignore the uncertainty of the environment model, which is ubiquitous in practical scenarios. In this work, we develop a theoretical solution to Markov games with environment model uncertainty. Specifically, we propose a new and tractable notion of robust correlated equilibria for Markov games with environment model uncertainty. In particular, we prove that the robust correlated equilibrium has a simple modification structure, and its characterization of equilibria critically depends on the environment model uncertainty. Moreover, we propose the first fully-decentralized stochastic algorithm for computing such the robust correlated equilibrium. Our analysis proves that the algorithm achieves the polynomial episode complexity $\widetilde{O}( SA^2 H^5 \epsilon^{-2})$ for computing an approximate robust correlated equilibrium with $\epsilon$ accuracy.