When are Offline Two-Player Zero-Sum Markov Games Solvable?

We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for learning the Nash equilibrium (NE) strategy in offline twoplayer zero-sum Markov games. On the other hand, we propose a new assumption named unilateral concentration and design a pessimism-type algorithm that is provably efficient under this assumption. In addition, we show that the unilateral concentration assumption is necessary for learning an NE strategy. Furthermore, our algorithm can achieve minimax sample complexity without any modification for two widely studied settings: dataset with uniform concentration assumption and turn-based Markov games. Our work serves as an important initial step towards understanding offline multi-agent reinforcement learning. learning process [Zhang et al., 2021a]. Specifically, the performance may decline if each agent simultaneously tries to improve its own policy depending on others' current policies. In addition, multiple agents incur complicated statistical dependence that makes the theoretical analysis difficult. A line of works study Markov games with online sampling oracle [