@article{bubeck2015sampling,
author = {Bubeck, Sébastien and Eldan, Ronen and Lehec, Joseph},
title = {Sampling from a log-concave distribution with Projected Langevin Monte Carlo},
year = {2015},
month = {July},
abstract = {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~(n7) 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~(n4) was proved by Lov[\'a]sz and Vempala.},
url = {http://approjects.co.za/?big=en-us/research/publication/sampling-log-concave-distribution-projected-langevin-monte-carlo/},
}