LEAD: Min-Max Optimization from a Physical Perspective

Reyhane Askari Hemmat, Amartya Mitra, Guillaume Lajoie, Ioannis Mitliagkas

Event Certifications: iclr.cc/ICLR/2024/Journal_Track

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.

Certifications: Featured Certification

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

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Video: https://www.youtube.com/watch?v=EfwIc0GXb8E

Code: https://github.com/ReyhaneAskari/Least_action_dynamics_minmax

Assigned Action Editor: ~Francisco_J._R._Ruiz1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 900