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Analysis of Langevin Monte Carlo via Convex Optimization

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dc.abstract.enIn this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as the first order optimization algorithm for an objective functional defined on the Wasserstein space of order 2. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from log-concave smooth target distribution on R d . Based on this interpretation, we propose two new methods for sampling from a non-smooth target distribution. These new algorithms are natural extensions of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm, which is a popular extension of the Unadjusted Langevin Algorithm for largescale Bayesian inference. Using the optimization perspective, we provide non-asymptotic convergence analysis for the newly proposed methods.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorMiasojedow, Błażej
dc.contributor.authorMajewski, Szymon
dc.contributor.authorDurmus, Alain
dc.date.accessioned2024-01-24T16:29:26Z
dc.date.available2024-01-24T16:29:26Z
dc.date.issued2019
dc.description.accesstimeAT_PUBLICATION
dc.description.financeNie dotyczy
dc.description.number73
dc.description.versionFINAL_PUBLISHED
dc.description.volume20
dc.identifier.issn1532-4435
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/100618
dc.identifier.weblinkhttp://www.jmlr.org/papers/v20/18-173.html
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofJournal of Machine Learning Research
dc.relation.pages1-46
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enUnadjasted Langevin Algorithm
dc.subject.enconvex optimization
dc.subject.enBayesian inference
dc.subject.engradient flow
dc.subject.enWasserstein metric
dc.titleAnalysis of Langevin Monte Carlo via Convex Optimization
dc.typeJournalArticle
dspace.entity.typePublication