Forward-reflected-backward method with variance reduction

Ahmet Alacaoglu (), Yura Malitsky () and Volkan Cevher ()
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Ahmet Alacaoglu: École Polytechnique Fédérale de Lausanne (EPFL)
Yura Malitsky: Linköping University
Volkan Cevher: École Polytechnique Fédérale de Lausanne (EPFL)

Computational Optimization and Applications, 2021, vol. 80, issue 2, No 1, 346 pages

Abstract: Abstract 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.

Keywords: Variational inequalities; Stochastic variance reduction; Finite-sum structure; Saddle point problems; Monotone inclusions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-021-00305-3

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