Training Generative Adversarial Networks via Stochastic Nash Games

Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. These two neural networks compete against each other through an adversarial process that can be modeled as a stochastic Nash equilibrium problem. Since the associated training process is challenging, it is fundamental to design reliable algorithms to compute an equilibrium. In this article, we propose a stochastic relaxed forward-backward (SRFB) algorithm for GANs, and we show convergence to an exact solution when an increasing number of data is available. We also show convergence of an averaged variant of the SRFB algorithm to a neighborhood of the solution when only a few samples are available. In both cases, convergence is guaranteed when the pseudogradient mapping of the game is monotone. This assumption is among the weakest known in the literature. Moreover, we apply our algorithm to the image generation problem.