Stochastic Forward–Backward Splitting for Monotone Inclusions

Lorenzo Rosasco (), Silvia Villa () and Bang Công Vũ ()
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Lorenzo Rosasco: Università di Genova
Silvia Villa: Istituto Italiano di Tecnologia and Massachusetts Institute of Technology
Bang Công Vũ: Istituto Italiano di Tecnologia and Massachusetts Institute of Technology

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 2, No 3, 388-406

Abstract: 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.

Keywords: Stochastic first-order methods; Forward–backward splitting algorithm; Monotone inclusions; Stochastic Fejér sequences; 47H05; 90C15; 65K10; 90C25 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0893-2

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