Two steps at a time -- taking GAN training in stride with Tseng's method

TL;DR

This paper introduces and analyzes two gradient-based methods for solving minimax problems with nonsmooth regularizers, improving convergence and computational efficiency, and demonstrates their effectiveness in training Wasserstein GANs.

Contribution

It proposes a new gradient recycling scheme related to OGDA, provides novel convergence rates for these methods, and applies them to GAN training.

Findings

Convergence rate of O(1/k) for deterministic problems.

Convergence rate of O(1/√k) for stochastic problems.

Empirical improvements in Wasserstein GAN training on CIFAR10.

Abstract

Motivated by the training of Generative Adversarial Networks (GANs), we study methods for solving minimax problems with additional nonsmooth regularizers. We do so by employing \emph{monotone operator} theory, in particular the \emph{Forward-Backward-Forward (FBF)} method, which avoids the known issue of limit cycling by correcting each update by a second gradient evaluation. Furthermore, we propose a seemingly new scheme which recycles old gradients to mitigate the additional computational cost. In doing so we rediscover a known method, related to \emph{Optimistic Gradient Descent Ascent (OGDA)}. For both schemes we prove novel convergence rates for convex-concave minimax problems via a unifying approach. The derived error bounds are in terms of the gap function for the ergodic iterates. For the deterministic and the stochastic problem we show a convergence rate of $\mathcal{O}(1/k)$ and $\mathcal{O}(1/\sqrt{k})$, respectively. We complement our theoretical results with empirical improvements in the training of Wasserstein GANs on the CIFAR10 dataset.