A Fixed-Point of View on Gradient Methods for Big Data

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorJung, Alexander
dc.contributor.departmentDepartment of Computer Science
dc.date.accessioned2018-02-09T10:06:48Z
dc.date.available2018-02-09T10:06:48Z
dc.date.issued2017
dc.description.abstractInterpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive datasets (big data). In particular, stochastic gradient methods are considered the defacto standard for training deep neural networks. Studying gradient methods within the realm of fixed-point theory provides us with powerful tools to analyze their convergence properties. In particular, gradient methods using inexact or noisy gradients, such as stochastic gradient descent, can be studied conveniently using well-known results on inexact fixed-point iterations. Moreover, as we demonstrate in this paper, the fixed-point approach allows an elegant derivation of accelerations for basic gradient methods. In particular, we will show how gradient descent can be accelerated by a fixed-point preserving transformation of an operator associated with the objective function.en
dc.description.versionPeer revieweden
dc.format.extent11
dc.format.extent1-11
dc.format.mimetypeapplication/pdf
dc.identifier.citationJung , A 2017 , ' A Fixed-Point of View on Gradient Methods for Big Data ' , Frontiers in Applied Mathematics and Statistics , vol. 3 , pp. 1-11 . https://doi.org/10.3389/fams.2017.00018en
dc.identifier.doi10.3389/fams.2017.00018
dc.identifier.issn2297-4687
dc.identifier.otherPURE UUID: d9ff3a44-e7a8-4c26-858f-c3980b3198ea
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/d9ff3a44-e7a8-4c26-858f-c3980b3198ea
dc.identifier.otherPURE LINK: https://www.frontiersin.org/article/10.3389/fams.2017.00018
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/16832497/fams_03_00018.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/30001
dc.identifier.urnURN:NBN:fi:aalto-201802091498
dc.language.isoenen
dc.relation.ispartofseriesFrontiers in Applied Mathematics and Statisticsen
dc.relation.ispartofseriesVolume 3en
dc.rightsopenAccessen
dc.subject.keywordconvex optimization
dc.subject.keywordfixed point theory
dc.subject.keywordbig data
dc.subject.keywordmachine learning
dc.subject.keywordcontraction mapping
dc.subject.keywordgradient descent
dc.subject.keywordheavy balls
dc.titleA Fixed-Point of View on Gradient Methods for Big Dataen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
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