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

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 monotone operator theory, in particular the 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 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 O( 1 /k) and O( 1 / √ k), respectively. We complement our theoretical results with empirical improvements in the training of Wasserstein GANs on the CIFAR10 dataset.Preprint. Under review.

Stochastic Variance Reduction for Variational Inequality Methods

“…But when not, FBF applied to the VI requires one proximal operator every iteration, whereas extragradient requires two. This advantage can be important for the cases where proximal operator is computationally expensive [Böh+20]. We have essentially the same convergence result as for extragradient in Section 2.3.…”

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

“…It is well known that while OGDA requires only half as many gradient evaluations per iterations compared to EG, it also asks for a smaller stepsize, see [6,46]. In the monotone (convex-concave) setting typical bounds on the stepsize are 1/L and 1/(2L) for EG and OGDA, respectively, see [6,46]. The downside of a smaller stepsize is typically a worse constant in the convergence rate.…”

“…Note that OGDA is most commonly written in the form where β = 1 is used, see [6,17,43], with the exception of two recent works which have investigated a more general coefficient see [45,55]. However, there, and for related methods [11,28,31], the parameter β is usually restricted to be less than 1.…”

Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers

“…The papers [68] and [54] consider stochastic variants of three-operator splitting, but they can only be applied to optimization problems. The methods of [70] and [7] can be applied to simple saddle-point problems involving a single regularizer.…”