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：对抗性公式（如生成对抗网络）重新激发了人们对双人极小极大博弈的兴趣。此类博弈优化中的一个核心障碍是阻碍其收敛的旋转动力学。本文表明，博弈优化与受多力作用的粒子系统具有共同的动力学特性，人们可以利用物理学工具改进优化动力学。受物理框架启发，我们提出了极小极大博弈优化器LEAD。接着，利用李雅普诺夫稳定性理论和谱分析，我们研究了LEAD在一类二次极小极大博弈中连续与离散时间设置下的收敛性质，证明其能线性收敛至纳什均衡。最后，我们在合成场景和CIFAR-10图像生成任务上进行了实证评估，展示了该方法对GAN训练的改进效果。