Shuffling Gradient-Based Methods for Nonconvex-Concave Minimax Optimization

TL;DR

This paper introduces novel shuffling gradient-based algorithms for nonconvex minimax problems, achieving state-of-the-art complexity bounds and demonstrating competitive performance with SGD through numerical experiments.

Contribution

The paper develops new shuffling gradient methods for nonconvex minimax problems, providing the first complexity bounds for these settings and introducing a new hyper-gradient shuffling estimator.

Findings

Algorithms achieve state-of-the-art oracle complexity.

Numerical results show competitive performance with SGD.

New shuffling estimator improves hyper-gradient estimation.

Abstract

This paper aims at developing novel shuffling gradient-based methods for tackling two classes of minimax problems: nonconvex-linear and nonconvex-strongly concave settings. The first algorithm addresses the nonconvex-linear minimax model and achieves the state-of-the-art oracle complexity typically observed in nonconvex optimization. It also employs a new shuffling estimator for the "hyper-gradient", departing from standard shuffling techniques in optimization. The second method consists of two variants: semi-shuffling and full-shuffling schemes. These variants tackle the nonconvex-strongly concave minimax setting. We establish their oracle complexity bounds under standard assumptions, which, to our best knowledge, are the best-known for this specific setting. Numerical examples demonstrate the performance of our algorithms and compare them with two other methods. Our results show that the new methods achieve comparable performance with SGD, supporting the potential of incorporating shuffling strategies into minimax algorithms.