Convergence of Gradient Methods on Bilinear Zero-Sum Games

Guojun Zhang, Yaoliang Yu

TL;DR: We systematically analyze the convergence of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates.

Abstract: Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.

Code: https://github.com/Gordon-Guojun-Zhang/ICLR-2020

Keywords: GAN, gradient algorithm, convergence, min-max optimization, bilinear game