LEAD: Min-Max Optimization from a Physical Perspective

TL;DR

This paper introduces LEAD, a physics-inspired optimizer for min-max games like GANs, leveraging particle system dynamics and stability analysis to improve convergence and training stability.

Contribution

We propose LEAD, a novel optimizer based on physical principles, with theoretical convergence guarantees and empirical improvements in GAN training.

Findings

LEAD achieves linear convergence in quadratic min-max games.

LEAD improves GAN training stability and convergence.

Empirical results show better performance on CIFAR-10.

Abstract

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.