Accelerated Proximal Alternating Gradient-Descent-Ascent for Nonconvex Minimax Machine Learning

Abstract

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the existing studies show that it suffers from a high computation complexity in nonconvex minimax optimization. In this paper, we develop a single-loop and fast AltGDA-type algorithm that leverages proximal gradient updates and momentum acceleration to solve regularized nonconvex minimax optimization problems. By leveraging the momentum acceleration technique, we prove that the algorithm converges to a critical point in nonconvex minimax optimization and achieves a computation complexity in the order of $\mathcal{O}(\kappa^{\frac{11}{6}}\epsilon^{-2})$, where $\epsilon$ is the desired level of accuracy and $\kappa$ is the problem's condition number. {Such a computation complexity improves the state-of-the-art complexities of single-loop GDA and AltGDA algorithms (see the summary of comparison in \Cref{table1})}. We demonstrate the effectiveness of our algorithm via an experiment on adversarial deep learning.