SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities

TL;DR

This paper introduces a SARAH-based variance reduction algorithm for stochastic finite-sum cocoercive variational inequalities, demonstrating linear convergence in strongly monotone cases and validating its practical effectiveness through experiments.

Contribution

The paper develops a novel SARAH-based method tailored for stochastic cocoercive variational inequalities, achieving linear convergence for strongly monotone problems.

Findings

Achieves linear convergence for strongly monotone problems

Validates the approach with practical experiments

Enhances stochastic variational inequality solving methods

Abstract

Variational inequalities are a broad formalism that encompasses a vast number of applications. Motivated by applications in machine learning and beyond, stochastic methods are of great importance. In this paper we consider the problem of stochastic finite-sum cocoercive variational inequalities. For this class of problems, we investigate the convergence of the method based on the SARAH variance reduction technique. We show that for strongly monotone problems it is possible to achieve linear convergence to a solution using this method. Experiments confirm the importance and practical applicability of our approach.