A Unified Convergence Analysis of Stochastic Bregman Proximal Gradient and Extragradient Methods

We consider a mini-batch stochastic Bregman proximal gradient method and a mini-batch stochastic Bregman proximal extragradient method for stochastic convex composite optimization problems. A simplified and unified convergence analysis framework is proposed to obtain almost sure convergence properti...

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Veröffentlicht in:Journal of optimization theory and applications 2021-03, Vol.188 (3), p.605-627
1. Verfasser: Xiao, Xiantao
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider a mini-batch stochastic Bregman proximal gradient method and a mini-batch stochastic Bregman proximal extragradient method for stochastic convex composite optimization problems. A simplified and unified convergence analysis framework is proposed to obtain almost sure convergence properties and expected convergence rates of the mini-batch stochastic Bregman proximal gradient method and its variants. This framework can also be used to analyze the convergence of the mini-batch stochastic Bregman proximal extragradient method, which has seldom been discussed in the literature. We point out that the standard uniformly bounded variance assumption and the usual Lipschitz gradient continuity assumption are not required in the analysis.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01799-3