PAC Learnability of Approximate Nash Equilibrium in Bimatrix Games

Computing Nash equilibrium in bimatrix games is PPAD-hard, and many works have focused on the approximate solutions. When games are generated from a fixed unknown distribution, learning a Nash predictor via data-driven approaches can be preferable. In this paper, we study the learnability of approximate Nash equilibrium in bimatrix games. We prove that Lipschitz function class is agnostic Probably Approximately Correct (PAC) learnable with respect to Nash approximation loss. Additionally, to demonstrate the advantages of learning a Nash predictor, we develop a model that can efficiently approximate solutions for games under the same distribution. We show by experiments that the solutions from our Nash predictor can serve as effective initializing points for other Nash solvers.