Learning in Zero-Sum Markov Games: Relaxing Strong Reachability and Mixing Time Assumptions (2312.08008v3)

Abstract: We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions nor sharing information. Prior works established finite-time convergence to an approximate Nash equilibrium under strong reachability and mixing time assumptions. We propose a convergent algorithm that significantly relaxes these assumptions, requiring only the existence of a single policy (not necessarily known) with bounded reachability and mixing time. Our key technical novelty is introducing Tsallis entropy regularization to smooth the best-response policy updates. By suitably tuning this regularization, we ensure sufficient exploration, thus bypassing previous stringent assumptions on the MDP. By establishing novel properties of the value and policy updates induced by the Tsallis entropy regularizer, we prove finite-time convergence to an approximate Nash equilibrium.