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On the discrepancy principle for stochastic gradient descent

Jahn, T; Jin, B; (2020) On the discrepancy principle for stochastic gradient descent. Inverse Problems , 36 (9) , Article 095009. 10.1088/1361-6420/abaa58. Green open access

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Abstract

Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale inverse problems. However, its theoretical properties remain largely underexplored in the lens of classical regularization theory. In this note, we study the classical discrepancy principle, one of the most popular a posteriori choice rules, as the stopping criterion for SGD, and prove the finite-iteration termination property and the convergence of the iterate in probability as the noise level tends to zero. The theoretical results are complemented with extensive numerical experiments.

Type: Article
Title: On the discrepancy principle for stochastic gradient descent
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/abaa58
Publisher version: https://doi.org/10.1088/1361-6420/abaa58
Language: English
Additional information: © 2020 IOP Publishing. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10106687
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