Variance-reduction for Variational Inequality Problems with Bregman Distance Function

TL;DR

This paper proposes a new stochastic variance-reduced algorithm for variational inequalities using Bregman distances, achieving optimal convergence and improved complexity, with demonstrated superior performance in experiments.

Contribution

Introduces a novel single-loop variance-reduction algorithm for VI problems with Bregman distances, offering optimal convergence guarantees and better complexity analysis.

Findings

Algorithm achieves optimal convergence rates.

Significant complexity improvements over existing methods.

Numerical experiments confirm superior performance.

Abstract

In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence guarantee under a monotone setting. Additionally, we explore a structured class of non-monotone problems that exhibit weak Minty solutions, and analyze the complexity of our proposed method, highlighting a significant improvement over existing approaches. Numerical experiments are presented to demonstrate the performance of our algorithm compared to state-of-the-art methods