Variance-reduction for Variational Inequality Problems with Bregman Distance Function

Zeinab Alizadeh; Erfan Yazdandoost Hamedani; Afrooz Jalilzadeh

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arXiv · 2405.10735

Variance-reduction for Variational Inequality Problems with Bregman Distance Function

Zeinab Alizadeh·Erfan Yazdandoost Hamedani·Afrooz Jalilzadeh

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Abstract

In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence guarantee under a monotone setting. Additionally, we explore a structured class of non-monotone problems that exhibit weak Minty solutions, and analyze the complexity of our proposed method, highlighting a significant improvement over existing approaches. Numerical experiments are presented to demonstrate the performance of our algorithm compared to state-of-the-art methods

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Zeinab Alizadeh, Erfan Yazdandoost Hamedani, Afrooz Jalilzadeh. 2024-05-17. Variance-reduction for Variational Inequality Problems with Bregman Distance Function. https://arxiv.org/abs/2405.10735

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