Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent

Arnak Dalalyan

No 2017-21, Working Papers from Center for Research in Economics and Statistics

Abstract: In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the convergence is measured in the Wasserstein distance and provide further insights on the very tight relations between, on the one hand, the Langevin Monte Carlo for sampling and, on the other hand, the gradient descent for optimization. Finally, we also establish guarantees for the convergence of a version of the Langevin Monte Carlo algorithm that is based on noisy evaluations of the gradient

Keywords: Markov Chain Monte Carlo; Approximate sampling; Rates of convergence; Langevin algorithm; Gradient descent (search for similar items in EconPapers)
Pages: 12 pages
Date: 2017-07-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://crest.science/RePEc/wpstorage/2017-21.pdf CREST working paper version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:crs:wpaper:2017-21

Access Statistics for this paper

More papers in Working Papers from Center for Research in Economics and Statistics Contact information at EDIRC.
Bibliographic data for series maintained by Secretariat General () and Murielle Jules Maintainer-Email : murielle.jules@ensae.Fr.