Shuffling Gradient Descent-Ascent with Variance Reduction for Nonconvex-Strongly Concave Smooth Minimax Problems

TL;DR

This paper introduces a novel stochastic gradient descent-ascent algorithm with shuffling and variance reduction for nonconvex-strongly concave minimax problems, achieving optimal complexity and superior empirical performance.

Contribution

It presents a new single-loop GDA algorithm combining shuffling schemes and variance reduction, matching best-known complexities and outperforming existing methods.

Findings

Achieves $oxed{ ext{O}( ext{kappa}^2 ext{epsilon}^{-2})}$ iteration complexity.

Outperforms existing shuffling schemes in theory.

Demonstrates superior empirical performance in experiments.

Abstract

In recent years, there has been considerable interest in designing stochastic first-order algorithms to tackle finite-sum smooth minimax problems. To obtain the gradient estimates, one typically relies on the uniform sampling-with-replacement scheme or various sampling-without-replacement (also known as shuffling) schemes. While the former is easier to analyze, the latter often have better empirical performance. In this paper, we propose a novel single-loop stochastic gradient descent-ascent (GDA) algorithm that employs both shuffling schemes and variance reduction to solve nonconvex-strongly concave smooth minimax problems. We show that the proposed algorithm achieves $\epsilon$-stationarity in expectation in $\mathcal{O}(\kappa^2 \epsilon^{-2})$ iterations, where $\kappa$ is the condition number of the problem. This outperforms existing shuffling schemes and matches the complexity of the best-known sampling-with-replacement algorithms. Our proposed algorithm also achieves the same complexity as that of its deterministic counterpart, the two-timescale GDA algorithm. Our numerical experiments demonstrate the superior performance of the proposed algorithm.