Towards the PAC Learnability of Nash Equilibrium

Nash equilibrium (NE) is one of the most important solution concepts in game theory and has broad applications in machine learning research. While tremendous empirical success has been reported on learning approximate NE, whether NE is Probably Approximately Correct (PAC) learnable has not been addressed yet. In this paper, we make the first effort to study the PAC learnability of NE in normal-form games. We prove that NE is agnostic PAC learnable if the hypothesis class for Nash predictors has bounded covering numbers. Theoretically, we derive such a result by constructing a self-supervised PAC learning framework based on a commonly-used objective for Nash approximation. Empirically, we provide numerical evidence showing that a Nash predictor trained under our PAC learning framework, even with the most straightforward neural architecture, can efficiently learn the NE for games sampled from the same unknown distribution. Our results justify the feasibility of approximating NE through purely data-driven approaches, which benefits both game theorists and machine learning practitioners.