Solve Minimax Optimization by Anderson Acceleration [preprint]

Preprint date

October 6, 2021

Authors

Huan He, Shifan Zhao, Yuanzhe Xi, Joyce C Ho, Yousef Saad (professor)

Abstract

Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its simplicity. However, GDA can converge to non-optimal minimax points. We propose a new minimax optimization framework, GDA-AM, that views the GDAdynamics as a fixed-point iteration and solves it using Anderson Mixing to con-verge to the local minimax. It addresses the diverging issue of simultaneous GDAand accelerates the convergence of alternating GDA. We show theoretically that the algorithm can achieve global convergence for bilinear problems under mild conditions. We also empirically show that GDA-AMsolves a variety of minimax problems and improves GAN training on several datasets

Link to full paper

Solve Minimax Optimization by Anderson Acceleration

Keywords

machine learning, generative adversarial networks