Adversarial formulations such as generative adversarial networks (GANs) have
rekindled interest in two-player min-max games. A central obstacle in the
optimization of such games is the rotational dynamics that hinder their
convergence. In this paper, we show that game optimization shares dynamic
properties with particle systems subject to multiple forces, and one can
leverage tools from physics to improve optimization dynamics. Inspired by the
physical framework, we propose LEAD, an optimizer for min-max games. Next,
using Lyapunov stability theory and spectral analysis, we study LEAD’s
convergence properties in continuous and discrete time settings for a class of
quadratic min-max games to demonstrate linear convergence to the Nash
equilibrium. Finally, we empirically evaluate our method on synthetic setups
and CIFAR-10 image generation to demonstrate improvements in GAN training.