Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities
Optimization and Control
2026-02-17 v1 Computer Science and Game Theory
Machine Learning
Abstract
We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax) problems, Nash equilibrium problems, and many others. The key challenges in our problem formulation are the two-level hierarchical structure and finite-sum representation of the smooth operators in each level. For this setting, we are the first to prove convergence rates and complexity statements for variance-reduced stochastic algorithms approaching the solution of hierarchical VIs in Euclidean and Bregman setups.
Cite
@article{arxiv.2602.13510,
title = {Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities},
author = {Pavel Dvurechensky and Andrea Ebner and Johannes Carl Schnebel and Shimrit Shtern and Mathias Staudigl},
journal= {arXiv preprint arXiv:2602.13510},
year = {2026}
}