Convergence of Stochastic Proximal Gradient Algorithm
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245_2019_9617_ReferencePDF.pdf
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Author(s)
Rosasco, Lorenzo
Villa, Silvia
Vũ, Bằng C
Date Issued
October 15, 2019
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
We study the extension of the proximal gradient algorithm where only a stochastic gradient estimate is available and a relaxation step is allowed. We establish convergence rates for function values in the convex case, as well as almost sure convergence and convergence rates for the iterates under further convexity assumptions. Our analysis avoid averaging the iterates and error summability assumptions which might not be satisfied in applications, e.g. in machine learning. Our proofing technique extends classical ideas from the analysis of deterministic proximal gradient algorithms.
MIT Department
Center for Brains, Minds, and Machines
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DOI of Published Version
https://doi.org/10.1007/s00245-019-09617-7
