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Mathematics > Numerical Analysis

arXiv:2108.04429 (math)
[Submitted on 10 Aug 2021 (v1), last revised 17 Dec 2021 (this version, v2)]

Title:An Analysis of Stochastic Variance Reduced Gradient for Linear Inverse Problems

Authors:Bangti Jin, Zehui Zhou, Jun Zou
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Abstract:Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens of the classical regularization theory. We prove that for a suitable constant step size schedule, the method can achieve an optimal convergence rate in terms of the noise level (under suitable regularity condition) and the variance of the SVRG iterate error is smaller than that by SGD. These theoretical findings are corroborated by a set of numerical experiments.
Comments: 31 pages, 2 figures, to appear at Inverse Problems
Subjects: Numerical Analysis (math.NA); Optimization and Control (math.OC)
Cite as: arXiv:2108.04429 [math.NA]
  (or arXiv:2108.04429v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2108.04429
Related DOI: https://doi.org/10.1088/1361-6420/ac4428

Submission history

From: Bangti Jin [view email]
[v1] Tue, 10 Aug 2021 03:31:36 UTC (1,051 KB)
[v2] Fri, 17 Dec 2021 02:49:21 UTC (1,054 KB)
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