We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and forward-reflected-backward methods both in Euclidean and Bregman setups. All proposed methods converge in the same setting as their deterministic counterparts and they either match or improve the best-known complexities for solving structured min-max problems. Our results reinforce the correspondence between variance reduction in variational inequalities and minimization. We also illustrate the improvements of our approach with numerical evaluations on matrix games.
@article{arxiv.2102.08352,
title = {Stochastic Variance Reduction for Variational Inequality Methods},
author = {Ahmet Alacaoglu and Yura Malitsky},
journal= {arXiv preprint arXiv:2102.08352},
year = {2022}
}