Approximating Nash Equilibria in Normal-Form Games via Stochastic Optimization

TL;DR

This paper introduces a novel loss function for approximating Nash equilibria in normal-form games, enabling the use of stochastic optimization techniques with theoretical guarantees and improved empirical performance.

Contribution

It presents the first loss function suitable for unbiased Monte Carlo estimation, facilitating stochastic optimization for Nash equilibria with proven guarantees.

Findings

Stochastic gradient descent can outperform previous methods.

The proposed approach provides theoretical guarantees for approximation quality.

Experimental results validate the effectiveness of the new algorithms.

Abstract

We propose the first 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.