Sampling from a log-concave distribution with Projected Langevin Monte Carlo
Bubeck, Sébastien; Eldan, Ronen; Lehec, Joseph (2017), Sampling from a log-concave distribution with Projected Langevin Monte Carlo. https://basepub.dauphine.fr/handle/123456789/17068
Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-01428950Date
2017Series title
Cahier de recherche CEREMADE, Université Paris-DauphinePages
23
Metadata
Show full item recordAbstract (EN)
We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a log-concave distribution with smooth potential. This gives a new Markov chain to sample from a log-concave distribution. Our main result shows in particular that when the target distribution is uniform, LMC mixes in O(n 7) steps (where n is the dimension). We also provide preliminary experimental evidence that LMC performs at least as well as hit-and-run, for which a better mixing time of O(n 4) was proved by Lovász and Vempala.Subjects / Keywords
Langevin Monte Carlo algorithm; Stochastic Gradient DescentRelated items
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