{"paper":{"title":"An Optimal Agnostic PAC Algorithm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.DS","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Jian Qian, Markus Engelund Mathiasen, Nikita Zhivotovskiy","submitted_at":"2026-08-06T17:57:25Z","abstract_excerpt":"Let $H\\subseteq\\{-1,+1\\}^X$ be a class of finite VC dimension $d\\ge1$. Writing $L$ for the binary risk and $L^*=\\min_{h\\in H}L(h)$, we construct a learner achieving the statistically optimal risk bound: from an i.i.d.\\ sample of size $n$, for every $0<\\delta\\le 1/2$, with probability at least $1-\\delta$, \\[\n  L(\\widehat h)\n  \\le L^*+ 7\\cdot10^8\\left(\n  \\sqrt{\\frac{L^*(d+\\log(1/\\delta))}{n}}\n  +\\frac{d+\\log(1/\\delta)}{n}\n  \\right). \\] This settles the sample complexity of agnostic PAC learning up to universal constants at every fixed $L^*$, matching the lower bounds of Devroye, Gy\\\"orfi, and Lu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06363","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/2608.06363/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"}