Approximating Nash Equilibria in Normal-Form Games via Unbiased Stochastic Optimization

Ian Gemp, Luke Marris, Georgios Piliouras

Keywords: game theory, stochastic optimization, nash equilbrium, normal-form game, x-armed bandits

TL;DR: We propose the first stochastic NE loss for normal-form games.

Abstract: We propose the first, to our knowledge, loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for approximating Nash equilibria, resulting in novel algorithms with provable guarantees. We complement our theoretical analysis with experiments demonstrating that stochastic gradient descent can outperform previous state-of-the-art approaches.

Submission Number: 5012