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.

翻译：对抗性框架（如生成对抗网络，GANs）重新激发了对双人极小极大博弈的关注。此类博弈优化中的核心障碍在于阻碍收敛的旋转动力学。本文表明，博弈优化与受多力作用的粒子系统具有相同的动态属性，因此可借助物理学工具改进优化动力学。受该物理框架启发，我们提出LEAD——一种面向极小极大博弈的优化器。随后，利用李雅普诺夫稳定性理论和谱分析，我们在连续与离散时间设置下研究了一类二次型极小极大博弈中LEAD的收敛性质，证明了其线性收敛至纳什均衡。最后，我们在合成实验和CIFAR-10图像生成任务上对方法进行实证评估，展示了其在GAN训练中的改进效果。