Show simple item record

dc.contributor.authorLoizou, Nicolas
dc.contributor.authorRichtarik, Peter
dc.date.accessioned2021-01-20T12:45:31Z
dc.date.available2019-11-27T10:42:15Z
dc.date.available2021-01-20T12:45:31Z
dc.date.issued2020-12-15
dc.date.submitted2019-03-25
dc.identifier.citationLoizou, N., & Richtárik, P. (2020). Convergence Analysis of Inexact Randomized Iterative Methods. SIAM Journal on Scientific Computing, 42(6), A3979–A4016. doi:10.1137/19m125248x
dc.identifier.issn1095-7197
dc.identifier.issn1064-8275
dc.identifier.doi10.1137/19M125248X
dc.identifier.urihttp://hdl.handle.net/10754/660271
dc.description.abstractIn this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods for solving three closely related problems: a convex stochastic quadratic optimization problem, a best approximation problem, and its dual, a concave quadratic maximization problem. Among the methods studied are stochastic gradient descent, stochastic Newton, stochastic proximal point, and stochastic subspace ascent. A common feature of these methods is that in their update rule a certain subproblem needs to be solved exactly. We relax this requirement by allowing for the subproblem to be solved inexactly. We provide iteration complexity results under several assumptions on the inexactness error. Inexact variants of many popular and some more exotic methods, including randomized block Kaczmarz, Gaussian block Kaczmarz, and randomized block coordinate descent, can be cast as special cases. Numerical experiments demonstrate the benefits of allowing inexactness.
dc.description.sponsorshipThe authors would like to acknowledge Robert Mansel Gower, Georgios Loizou, Aritra Dutta, and Rachael Tappenden for useful discussions.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/19M125248X
dc.rightsPublished by SIAM under the terms of the Creative Commons 4.0 license.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectInexact methodsen_US
dc.titleConvergence analysis of inexact randomized iterative methods
dc.typeArticle
dc.contributor.departmentComputer Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionMila and DIRO, Université de Montréal, Montreal, Quebec, H2S 3H1, Canada
dc.identifier.volume42
dc.identifier.issue6
dc.identifier.pagesA3979-A4016
dc.identifier.arxivid1903.07971
kaust.personRichtarik, Peter
dc.date.accepted2020-08-19
dc.identifier.eid2-s2.0-85099065193
refterms.dateFOA2019-11-27T10:42:44Z


Files in this item

Thumbnail
Name:
19m125248x.pdf
Size:
1.248Mb
Format:
PDF
Description:
Publisher's version

This item appears in the following Collection(s)

Show simple item record

Published by SIAM under the terms of the Creative Commons 4.0 license.
Except where otherwise noted, this item's license is described as Published by SIAM under the terms of the Creative Commons 4.0 license.
VersionItemEditorDateSummary

*Selected version