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hal.structure.identifierCentre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
dc.contributor.authorHu, Kaitong
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorKazeykina, Anna
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorRen, Zhenjie
dc.date.accessioned2019-09-20T12:00:41Z
dc.date.available2019-09-20T12:00:41Z
dc.date.issued2019-09
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19860
dc.language.isoenen
dc.subjectMean-Field Langevin Dynamicsen
dc.subjectGradient Flowen
dc.subjectNeural Networksen
dc.subject.ddc515en
dc.titleMean-field Langevin System, Optimal Control and Deep Neural Networksen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant measure of which is shown to be the optimal control of the initial problem under mild conditions. Therefore, this system of processes can be viewed as a continuous-time numerical algorithm for computing the optimal control. As an application, this result endorses the solvability of the stochastic gradient descent algorithm for a wide class of deep neural networks.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages25en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.contributor.countryeditoruniversityotherFRANCE
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-09
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-09-20T11:57:30Z
hal.identifierhal-02292984*
hal.version1*
hal.update.actionupdateFiles*
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