Convergence of Gradient Methods on Bilinear Zero-Sum Games
Machine Learning
2020-03-05 v4 Computer Science and Game Theory
Optimization and Control
Machine Learning
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.
Keywords
Cite
@article{arxiv.1908.05699,
title = {Convergence of Gradient Methods on Bilinear Zero-Sum Games},
author = {Guojun Zhang and Yaoliang Yu},
journal= {arXiv preprint arXiv:1908.05699},
year = {2020}
}