A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction

Andre Milzarek, Fabian Schaipp, Michael Ulbrich

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.

Original languageEnglish
Pages (from-to)1157-1185
JournalSIAM Journal on Optimization
Volume34
Issue number1
DOIs
StatePublished - 2024

Keywords

  • semismooth Newton
  • stochastic optimization
  • stochastic proximal point method

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