Is Nash Equilibrium Approximator Learnable?

TL;DR

This paper explores the theoretical feasibility and practical application of learning a function approximator for Nash equilibria in games, providing generalization bounds, learnability proofs, and experimental validation.

Contribution

It introduces the first theoretical analysis of NE approximator learnability, including PAC bounds and agnostic PAC learnability, with experimental demonstrations of acceleration in NE solving.

Findings

Established PAC generalization bounds for NE approximators

Proved the agnostic PAC learnability of Nash equilibrium functions

Demonstrated NE approximator's effectiveness in speeding up classical NE solvers

Abstract

In this paper, we investigate the learnability of the function approximator that approximates Nash equilibrium (NE) for games generated from a distribution. First, we offer a generalization bound using the Probably Approximately Correct (PAC) learning model. The bound describes the gap between the expected loss and empirical loss of the NE approximator. Afterward, we prove the agnostic PAC learnability of the Nash approximator. In addition to theoretical analysis, we demonstrate an application of NE approximator in experiments. The trained NE approximator can be used to warm-start and accelerate classical NE solvers. Together, our results show the practicability of approximating NE through function approximation.