{"paper":{"title":"On the relation between optimal transport and Schr\\\"odinger bridges: A stochastic control viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC","math.PR"],"primary_cat":"cs.SY","authors_text":"Michele Pavon, Tryphon Georgiou, Yongxin Chen","submitted_at":"2014-12-15T00:44:37Z","abstract_excerpt":"We take a new look at the relation between the optimal transport problem and the Schr\\\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing literature. In particular: a) We give an elementary derivation of the Benamou-Brenier fluid dynamics version of the optimal transport problem; b) We provide a new fluid dynamics version of the Schr\\\"{o}dinger bridge problem; c) We observe that the latter provides an important connection with optimal transport without zero noise limits; d) We propose and solve a fluid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4430","kind":"arxiv","version":1},"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"}