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Article Dans Une Revue Discrete and Computational Geometry Année : 2018

Sampling from a log-concave distribution with Projected Langevin Monte Carlo

Résumé

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.
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Dates et versions

hal-01428950 , version 1 (06-01-2017)

Identifiants

Citer

Sébastien Bubeck, Ronen Eldan, Joseph Lehec. Sampling from a log-concave distribution with Projected Langevin Monte Carlo. Discrete and Computational Geometry, 2018, 59 (4), pp.757-783. ⟨10.1007/s00454-018-9992-1⟩. ⟨hal-01428950⟩
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