Work

Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.13510

Authors: Dvurechensky, Pavel, Ebner, Andrea, Schnebel, Johannes Carl, Shtern, Shimrit, Staudigl, Mathias

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7129519969

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