Stochastic forward-backward and primal-dual approximation algorithms\n with application to online image restoration

2016/02/25 by Patrick L. Combettes, Combettes, Patrick L., Jean‐Christophe Pesquet +1
Computer Science · Engineering · Mathematics · #90C15 #90C25 #94A08 #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1602.08021

openalex publication_date 2016/02/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Stochastic approximation techniques have been used in various contexts in\ndata science. We propose a stochastic version of the forward-backward algorithm\nfor minimizing the sum of two convex functions, one of which is not necessarily\nsmooth. Our framework can handle stochastic approximations of the gradient of\nthe smooth function and allows for stochastic errors in the evaluation of the\nproximity operator of the nonsmooth function. The almost sure convergence of\nthe iterates generated by the algorithm to a minimizer is established under\nrelatively mild assumptions. We also propose a stochastic version of a popular\nprimal-dual proximal splitting algorithm, establish its convergence, and apply\nit to an online image restoration problem.\n

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