Stochastic Forward–Backward Splitting for Monotone Inclusions
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Author(s)
Villa, Silvia
Vũ, Bang Công
Rosasco, Lorenzo Andrea
Date Issued
February 2016
Journal
Journal of Optimization Theory and Applications
Publisher
Springer US
Citation
Rosasco, Lorenzo, Silvia Villa, and Bang Công Vũ. “Stochastic Forward–Backward Splitting for Monotone Inclusions.” Journal of Optimization Theory and Applications 169, no. 2 (February 18, 2016): 388–406.
Version
Author's final manuscript
Abstract
We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward–backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as well as almost sure convergence under weaker assumptions. For minimization problems, we recover rates matching those obtained by stochastic extensions of the so-called accelerated methods. Stochastic quasi-Fejér’s sequences are a key technical tool to prove almost sure convergence.
MIT Department
Massachusetts Institute of Technology. Laboratory for Computational and Statistical Learning
McGovern Institute for Brain Research at MIT
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10957-016-0893-2
