We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.
Type
research article
Web of Science ID
WOS:000649113800019
Authors
Ma, Yi-An
•
Chatterji, Niladri S.
•
Cheng, Xiang
•
•
Bartlett, Peter L.
•
Jordan, Michael, I
Publication date
2021-08-01
Published in
Volume
27
Issue
3
Start page
1942
End page
1992
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
June 19, 2021
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