Learning in Zero-Sum Markov Games: Relaxing Strong Reachability and Mixing Time Assumptions

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 polynomial-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 with bounded reachability and mixing time. Our key algorithmic 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. We prove a polynomial-time convergence to an approximate Nash equilibrium by establishing novel properties of the value and policy updates induced by the Tsallis entropy regularizer.

Authors

• Reda Ouhamma Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 - CRIStAL, F-59000
• Maryam Kamgarpour

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