{"paper":{"title":"Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alex Delalande, L\\'ena\\\"ic Chizat, Tomas Va\\v{s}kevi\\v{c}ius","submitted_at":"2024-07-01T11:49:30Z","abstract_excerpt":"We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\\mu$, admits a density over $\\mathbb{R}^d$. For a semi-concave cost function bounded by $c_{\\infty}$ and a regularization parameter $\\lambda > 0$, we obtain exponential convergence guarantees on the dual sub-optimality gap with contraction rate polynomial in $\\lambda/c_{\\infty}$. This represents an exponential improvement over the known contraction rate $1 - \\Theta(\\exp(-c_{\\infty}/\\lambda))$ achievable via Hilbert's projective metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01202","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.01202/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}