Forward-reflected-backward method with variance reduction

We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic averag...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 80; no. 2; pp. 321 - 346
Main Authors: Alacaoglu, Ahmet, Malitsky, Yura, Cevher, Volkan
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2021
Springer Nature B.V
Subjects:
Algorithms
Convergence
Convex and Discrete Geometry
Inclusions
Inequalities
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Finite-sum structure
Monotone inclusions
Stochastic variance reduction
Variational inequalities
Saddle point problems
ISSN:0926-6003, 1573-2894, 1573-2894
Online Access:Get full text
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Summary:We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O (1/ k ) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.
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ISSN:0926-6003
1573-2894
1573-2894
DOI:10.1007/s10589-021-00305-3