Beyond Local Nash Equilibria for Adversarial Networks

TL;DR

This paper introduces a game-theoretic approach to GAN training that guarantees convergence to a resource-bounded Nash equilibrium, improving stability and solution quality over traditional methods.

Contribution

It models GANs as finite games in mixed strategies and proposes a convergent solution method to find better equilibria with increased computational resources.

Findings

Reduces mode collapse in GAN training

Produces solutions less exploitable than traditional GANs

Aligns solutions closely with theoretical Nash equilibria

Abstract

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found generator or classifier. This paper proposes to model GANs explicitly as finite games in mixed strategies, thereby ensuring that every LNE is an NE. With this formulation, we propose a solution method that is proven to monotonically converge to a resource-bounded Nash equilibrium (RB-NE): by increasing computational resources we can find better solutions. We empirically demonstrate that our method is less prone to typical GAN problems such as mode collapse, and produces solutions that are less exploitable than those produced by GANs and MGANs, and closely resemble theoretical predictions about NEs.