{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-tamed-unadjusted-langevin-algorithm","title":"The Tamed Unadjusted Langevin Algorithm","arxiv_id":"1710.05559","date":"2017-10-16","proceeding":null,"authors":["Nicolas Brosse","Alain Durmus","Éric Moulines","Sotirios Sabanis"],"abstract":"In this article, we consider the problem of sampling from a probability measure $\\pi$ having a density on $\\mathbb{R}^d$ known up to a normalizing constant, $x\\mapsto \\mathrm{e}^{-U(x)} / \\int_{\\mathbb{R}^d} \\mathrm{e}^{-U(y)} \\mathrm{d} y$. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable in a precise sense, when the potential $U$ is superlinear, i.e. $\\liminf_{\\Vert x \\Vert\\to+\\infty} \\Vert \\nabla U(x) \\Vert / \\Vert x \\Vert = +\\infty$. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in $V$-total variation norm and Wasserstein distance of order $2$ between the iterates of TULA and $\\pi$, as well as weak error bounds. Numerical experiments are presented which support our findings.","url_abs":"http://arxiv.org/abs/1710.05559v3","url_pdf":"http://arxiv.org/pdf/1710.05559v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-tamed-unadjusted-langevin-algorithm","repo_url":"https://github.com/nbrosse/TULA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}