Stochastic Forward-Backward Splitting for Monotone Inclusions

• Main Authors: Villa, Silvia (Contributor), Vũ, Bang Công (Contributor), Rosasco, Lorenzo Andrea (Contributor)
• Other Authors: Massachusetts Institute of Technology. Laboratory for Computational and Statistical Learning (Contributor), McGovern Institute for Brain Research at MIT (Contributor)
• Format: Article
• Language: English
• Published: Springer US, 2016-07-01T18:13:14Z.
• Subjects: Article
• Online Access: Get fulltext

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.
Italy. Ministero dell'istruzione, dell'università e della ricerca (FIRB project RBFR12M3AC)
Vietnam. National Foundation for Science and Technology Development (Grant No. 102.01-2014.02)