Convergence of Gradient Methods on Bilinear Zero-Sum Games
This addresses a foundational challenge in understanding min-max optimization dynamics for ML applications like generative models and adversarial methods.
The paper analyzes gradient methods for bilinear zero-sum games, providing exact convergence conditions and optimal parameter setups with convergence rates, showing that alternating updates outperform simultaneous ones.
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.