Forward-reflected-backward method with variance reduction

Ahmet Alacaoglu, Yura Malitsky, Volkan Cevher
2021 Computational optimization and applications  
AbstractWe 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
more » ... We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.
doi:10.1007/s10589-021-00305-3 pmid:34720428 pmcid:PMC8550342 fatcat:dyctzkychrf2ndcc7axbrxml2q