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Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization
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Zhang, Ying, Akyildiz, Ömer Deniz, Damoulas, Theodoros and Sabanis, Sotirios (2023) Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization. Applied Mathematics and Optimization, 87 . 25. doi:10.1007/s00245-022-09932-6
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WRAP-nonasymptotic-estimates-Stochastic-Gradient-Langevin-Dynamics-under-local-conditions-nonconvex-optimization-Damoulas-2022.pdf - Accepted Version - Requires a PDF viewer. Download (997Kb) | Preview |
Official URL: https://doi.org/10.1007/s00245-022-09932-6
Abstract
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the aforementioned Wasserstein-2 convergence result can be applied to establish a nonasymptotic error bound for the expected excess risk. Crucially, these results are obtained under a local Lipschitz condition and a local dissipativity condition where we remove the uniform dependence in the data stream. We illustrate the importance of this relaxation by presenting examples from variational inference and from index tracking optimization.
Item Type: | Journal Article | ||||||||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Langevin equations, Brownian motion processes, Numerical analysis, Mathematical optimization, Sampling (Statistics), Algorithms | ||||||||||||||||||||||||||||||
Journal or Publication Title: | Applied Mathematics and Optimization | ||||||||||||||||||||||||||||||
Publisher: | Springer | ||||||||||||||||||||||||||||||
ISBN: | 0095-4616 | ||||||||||||||||||||||||||||||
Official Date: | 13 January 2023 | ||||||||||||||||||||||||||||||
Dates: |
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Volume: | 87 | ||||||||||||||||||||||||||||||
Article Number: | 25 | ||||||||||||||||||||||||||||||
DOI: | 10.1007/s00245-022-09932-6 | ||||||||||||||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||||||||||||||
Re-use Statement: | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00245-022-09932-6 | ||||||||||||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||||||||||||||
Date of first compliant deposit: | 14 October 2022 | ||||||||||||||||||||||||||||||
Date of first compliant Open Access: | 7 February 2023 | ||||||||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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