{"paper":{"title":"Uniform-in-time mean-field limit estimate for the Consensus-Based Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Hicham Kouhkouh, Hui Huang","submitted_at":"2024-11-06T15:25:42Z","abstract_excerpt":"We establish a uniform-in-time estimate for the mean-field convergence of the Consensus-Based Optimization (CBO) algorithm by rescaling the consensus point in the dynamics with a small parameter $\\kappa \\in (0,1)$. This uniform-in-time estimate is essential, as CBO convergence relies on a sufficiently large time horizon and is crucial for ensuring stable, reliable long-term convergence, the latter being key to the practical effectiveness of CBO methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03986","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/2411.03986/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"}