{"paper":{"title":"Sharp convergence rates for mean field control in the region of strong regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.OC","authors_text":"Joe Jackson, Nikiforos Mimikos-Stamatopoulos, Panagiotis E. Souganidis, Pierre Cardaliaguet","submitted_at":"2023-12-18T17:37:17Z","abstract_excerpt":"We study the convergence problem for mean field control, also known as optimal control of McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the limiting value function $\\mathcal{U} :[0,T] \\times \\mathcal{P}_2(\\mathbb{R}^d) \\to \\mathbb{R}$ is Lipschitz, but may not be differentiable. In this setting, the first and last named authors recently identified an open and dense subset $\\mathcal{O}$ of $[0,T] \\times \\mathcal{P}_2(\\mathbb{R}^d)$ on which $\\mathcal{U}$ is $\\mathcal{C}^1$ and solves the relevant infinite-dimensional Hamilton-Jacobi equation in a classical s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11373","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.11373/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"}