{"paper":{"title":"Underdamped Langevin MCMC: A non-asymptotic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.CO"],"primary_cat":"stat.ML","authors_text":"Michael I. Jordan, Niladri S. Chatterji, Peter L. Bartlett, Xiang Cheng","submitted_at":"2017-07-12T12:08:55Z","abstract_excerpt":"We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\\varepsilon$ error (in 2-Wasserstein distance) in $\\mathcal{O}(\\sqrt{d}/\\varepsilon)$ steps. This is a significant improvement over the best known rate for overdamped Langevin MCMC, which is $\\mathcal{O}(d/\\varepsilon^2)$ steps under the same smoothness/concavity assumptions.\n  The underdamped Langevin MCMC scheme can be viewed as a version of Hamiltonian Monte Carlo (HMC) which has been observed t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03663","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}