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Sampling and Update Frequencies in Proximal Variance-Reduced Stochastic Gradient Methods

Morin, Martin LU and Giselsson, Pontus LU orcid (2025) In Journal of Optimization Theory and Applications 205(3).
Abstract

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for storing and sampling gradients, and this work concerns the interactions between these two aspects. We present a general proximal variance-reduced gradient method and analyze it under strong convexity assumptions. Special cases of the algorithm include SAGA, L-SVRG, and their proximal variants. Our analysis sheds light on epoch-length selection and the need to balance the convergence of the iterates with how often gradients are stored. The analysis improves on other convergence rates found in the literature and produces a new and faster converging sampling strategy for SAGA. Problem instances for which... (More)

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for storing and sampling gradients, and this work concerns the interactions between these two aspects. We present a general proximal variance-reduced gradient method and analyze it under strong convexity assumptions. Special cases of the algorithm include SAGA, L-SVRG, and their proximal variants. Our analysis sheds light on epoch-length selection and the need to balance the convergence of the iterates with how often gradients are stored. The analysis improves on other convergence rates found in the literature and produces a new and faster converging sampling strategy for SAGA. Problem instances for which the predicted rates are the same as the practical rates are presented together with problems based on real-world data.

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Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Epoch length, L-SVRG, SAGA, Sampling, Stochastic gradient, Variance-reduced
in
Journal of Optimization Theory and Applications
volume
205
issue
3
article number
58
publisher
Springer
external identifiers
  • scopus:105003321216
ISSN
0022-3239
DOI
10.1007/s10957-025-02671-y
language
English
LU publication?
yes
id
20da8231-8e44-419f-b138-95c00ba98bbf
date added to LUP
2025-07-29 09:50:29
date last changed
2025-07-29 09:51:39
@article{20da8231-8e44-419f-b138-95c00ba98bbf,
  abstract     = {{<p>Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for storing and sampling gradients, and this work concerns the interactions between these two aspects. We present a general proximal variance-reduced gradient method and analyze it under strong convexity assumptions. Special cases of the algorithm include SAGA, L-SVRG, and their proximal variants. Our analysis sheds light on epoch-length selection and the need to balance the convergence of the iterates with how often gradients are stored. The analysis improves on other convergence rates found in the literature and produces a new and faster converging sampling strategy for SAGA. Problem instances for which the predicted rates are the same as the practical rates are presented together with problems based on real-world data.</p>}},
  author       = {{Morin, Martin and Giselsson, Pontus}},
  issn         = {{0022-3239}},
  keywords     = {{Epoch length; L-SVRG; SAGA; Sampling; Stochastic gradient; Variance-reduced}},
  language     = {{eng}},
  number       = {{3}},
  publisher    = {{Springer}},
  series       = {{Journal of Optimization Theory and Applications}},
  title        = {{Sampling and Update Frequencies in Proximal Variance-Reduced Stochastic Gradient Methods}},
  url          = {{http://dx.doi.org/10.1007/s10957-025-02671-y}},
  doi          = {{10.1007/s10957-025-02671-y}},
  volume       = {{205}},
  year         = {{2025}},
}