{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:36:19Z","timestamp":1771659379348,"version":"3.50.1"},"reference-count":97,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T00:00:00Z","timestamp":1718064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>\n            It is a fundamental problem to understand the complexity of high-accuracy sampling from a strongly log-concave density \u03c0 on \u211d\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            . Indeed, in practice, high-accuracy samplers such as the Metropolis-adjusted Langevin algorithm (MALA) remain the de facto gold standard; and in theory, via the proximal sampler reduction, it is understood that such samplers are key for sampling even beyond log-concavity (in particular, for sampling under isoperimetric assumptions).\n          <\/jats:p>\n          <jats:p>\n            This article improves the dimension dependence of this sampling problem to\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\widetilde{O}(d^{1\/2})\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            . The previous best result for MALA was\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\widetilde{O}(d)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            . This closes the long line of work on the complexity of MALA and, moreover, leads to state-of-the-art guarantees for high-accuracy sampling under strong log-concavity and beyond (thanks to the aforementioned reduction).\n          <\/jats:p>\n          <jats:p>\n            Our starting point is that the complexity of MALA improves to\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\widetilde{O}(d^{1\/2})\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            , but only under a\n            <jats:italic>warm start<\/jats:italic>\n            (an initialization with constant R\u00e9nyi divergence w.r.t. \u03c0). Previous algorithms for finding a warm start took\n            <jats:italic>O(d)<\/jats:italic>\n            time and thus dominated the computational effort of sampling. Our main technical contribution resolves this gap by establishing the first\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\widetilde{O}(d^{1\/2})\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            R\u00e9nyi mixing rates for the discretized underdamped Langevin diffusion. For this, we develop new differential-privacy-inspired techniques based on R\u00e9nyi divergences with Orlicz\u2013Wasserstein shifts, which allow us to sidestep longstanding challenges for proving fast convergence of hypocoercive differential equations.\n          <\/jats:p>","DOI":"10.1145\/3653446","type":"journal-article","created":{"date-parts":[[2024,3,20]],"date-time":"2024-03-20T12:08:04Z","timestamp":1710936484000},"page":"1-55","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Faster High-accuracy Log-concave Sampling via Algorithmic Warm Starts"],"prefix":"10.1145","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7367-0097","authenticated-orcid":false,"given":"Jason M.","family":"Altschuler","sequence":"first","affiliation":[{"name":"UPenn, Philadelphia, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2701-0703","authenticated-orcid":false,"given":"Sinho","family":"Chewi","sequence":"additional","affiliation":[{"name":"IAS, Princeton, USA"}]}],"member":"320","published-online":{"date-parts":[[2024,6,11]]},"reference":[{"key":"e_1_3_4_2_1","first-page":"265","volume-title":"Symposium on Operating Systems Design and Implementation","author":"Abadi Mart\u00edn","year":"2016","unstructured":"Mart\u00edn Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et\u00a0al. 2016a. 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