When is Offline Two-Player Zero-Sum Markov Game Solvable?
This work addresses a foundational gap in offline multi-agent reinforcement learning, providing initial insights into solvability conditions for two-player games.
The paper tackles the problem of determining dataset assumptions that allow solving offline two-player zero-sum Markov games, showing that single strategy concentration is insufficient while proposing a necessary unilateral concentration assumption and a provably efficient algorithm.
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 two-player 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.