Towards General Function Approximation in Zero-Sum Markov Games

Baihe Huang, Jason D. Lee, Zhaoran Wang, Zhuoran Yang

Abstract:

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. Our
algorithms are based on new techniques of alternate optimism