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

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.

38 pages, 1 algorithm, 4 figures, 1 table

References in corpus (4)

• Convex Sparse Matrix Factorizations
• Global Convergence and Variance-Reduced Optimization for a Class of Nonconvex-Nonconcave Minimax Problems
• Optimal Gradient Sliding and its Application to Distributed Optimization Under Similarity
• Continuous-time Analysis for Variational Inequalities: An Overview and Desiderata