Method with Batching for Stochastic Finite-Sum Variational Inequalities in Non-Euclidean Setting

TL;DR

This paper introduces a batching method for stochastic finite-sum variational inequalities that achieves optimal convergence, supports arbitrary Bregman distances, and is validated through experiments.

Contribution

It presents a novel batching algorithm for stochastic variational inequalities that maintains optimal oracle complexity and accommodates non-Euclidean geometries.

Findings

Supports batching without losing optimal complexity

Achieves optimal convergence rates for stochastic variational inequalities

Experimental results confirm algorithm's effectiveness

Abstract

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this paper, we present an analysis of a method that gives optimal convergence estimates for monotone stochastic finite-sum variational inequalities. In contrast to the previous works, our method supports batching, does not lose the oracle complexity optimality and uses an arbitrary Bregman distance to take into account geometry of the problem. Paper provides experimental confirmation to algorithm's effectiveness.