Towards General Function Approximation in Zero-Sum Markov Games
This work addresses efficient learning in complex Markov games, which is incremental as it extends existing methods to more general function classes with theoretical guarantees.
The paper tackles the problem of two-player zero-sum finite-horizon Markov games with general function approximation, developing provably efficient algorithms for decoupled and coordinated settings. In the decoupled setting, it introduces a model-free algorithm with sample complexity based on the Minimax Eluder dimension, improving state-of-the-art regret by a √d factor for linear features.
This paper considers two-player zero-sum finite-horizon Markov games with simultaneous moves. The study focuses on the challenging settings where the value function or the model is parameterized by general function classes. Provably efficient algorithms for both decoupled and {coordinated} settings are developed. In the {decoupled} setting where the agent controls a single player and plays against an arbitrary opponent, we propose a new model-free algorithm. The sample complexity is governed by the Minimax Eluder dimension -- a new dimension of the function class in Markov games. As a special case, this method improves the state-of-the-art algorithm by a $\sqrt{d}$ factor in the regret when the reward function and transition kernel are parameterized with $d$-dimensional linear features. In the {coordinated} setting where both players are controlled by the agent, we propose a model-based algorithm and a model-free algorithm. In the model-based algorithm, we prove that sample complexity can be bounded by a generalization of Witness rank to Markov games. The model-free algorithm enjoys a $\sqrt{K}$-regret upper bound where $K$ is the number of episodes.