{"paper":{"title":"Approximation rates of entropic maps in semidiscrete optimal transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Kengo Kato, Ritwik Sadhu, Ziv Goldfeld","submitted_at":"2024-11-12T17:19:25Z","abstract_excerpt":"Entropic optimal transport offers a computationally tractable approximation to the classical problem. In this note, we study the approximation rate of the entropic optimal transport map (in approaching the Brenier map) when the regularization parameter $\\varepsilon$ tends to zero in the semidiscrete setting, where the input measure is absolutely continuous while the output is finitely discrete. Previous work shows that the approximation rate is $O(\\sqrt{\\varepsilon})$ under the $L^2$-norm with respect to the input measure. In this work, we establish faster, $O(\\varepsilon^2)$ rates up to polyl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07947","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/2411.07947/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"}