SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities

Aleksandr Beznosikov; Alexander Gasnikov

doi:10.1007/978-3-031-31654-8_3

SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities

Optimization and Control 2023-09-26 v1 Machine Learning

Authors: Aleksandr Beznosikov , Alexander Gasnikov

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Abstract

Variational inequalities are a broad formalism that encompasses a vast number of applications. Motivated by applications in machine learning and beyond, stochastic methods are of great importance. In this paper we consider the problem of stochastic finite-sum cocoercive variational inequalities. For this class of problems, we investigate the convergence of the method based on the SARAH variance reduction technique. We show that for strongly monotone problems it is possible to achieve linear convergence to a solution using this method. Experiments confirm the importance and practical applicability of our approach.

Keywords

stochastic optimization randomized kaczmarz algorithm stochastic differential equations

Cite

@article{arxiv.2210.05994,
  title  = {SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities},
  author = {Aleksandr Beznosikov and Alexander Gasnikov},
  journal= {arXiv preprint arXiv:2210.05994},
  year   = {2023}
}

Comments

11 pages, 1 algorithm, 1 figure, 1 theorem

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