{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CQKIATQSJUVX3HH3GCU2IPRGCL","short_pith_number":"pith:CQKIATQS","schema_version":"1.0","canonical_sha256":"1414804e124d2b7d9cfb30a9a43e2612e07ff6816c376852bfe5d9c2de85a316","source":{"kind":"arxiv","id":"2608.06363","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.06363","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-06T17:57:25Z","cross_cats_sorted":["cs.AI","cs.DS","math.ST","stat.TH"],"title_canon_sha256":"4bf12211038afea5a931b0ac307bf3d8b659f420ffc0cbae06d41dd2555662db","abstract_canon_sha256":"c1e03d3a9b26402072eeb99f7498d41d402ab63cee34b3bfc8f60463f24a215d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T01:41:29.119223Z","signature_b64":"hdOVAOSoyyif7iCRjxslrjvJK4q1V7NWwAS/r97AEkad9gC68xCNn3HbsfHiRhvZOJmRfaZCdq0+d5otg0MnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1414804e124d2b7d9cfb30a9a43e2612e07ff6816c376852bfe5d9c2de85a316","last_reissued_at":"2026-08-07T01:41:29.117507Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T01:41:29.117507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.06363","created_at":"2026-08-07T01:41:29.120204+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.06363v1","created_at":"2026-08-07T01:41:29.120204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06363","created_at":"2026-08-07T01:41:29.120204+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQKIATQSJUVX","created_at":"2026-08-07T01:41:29.120204+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQKIATQSJUVX3HH3","created_at":"2026-08-07T01:41:29.120204+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQKIATQS","created_at":"2026-08-07T01:41:29.120204+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.10869","citing_title":"Optimistic Rates for Multiclass PAC Learning","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL","json":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL.json","graph_json":"https://pith.science/api/pith-number/CQKIATQSJUVX3HH3GCU2IPRGCL/graph.json","events_json":"https://pith.science/api/pith-number/CQKIATQSJUVX3HH3GCU2IPRGCL/events.json","paper":"https://pith.science/paper/CQKIATQS"},"agent_actions":{"view_html":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL","download_json":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL.json","view_paper":"https://pith.science/paper/CQKIATQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.06363&json=true","fetch_graph":"https://pith.science/api/pith-number/CQKIATQSJUVX3HH3GCU2IPRGCL/graph.json","fetch_events":"https://pith.science/api/pith-number/CQKIATQSJUVX3HH3GCU2IPRGCL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL/action/storage_attestation","attest_author":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL/action/author_attestation","sign_citation":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL/action/citation_signature","submit_replication":"https://pith.science/pith/CQKIATQSJUVX3HH3GCU2IPRGCL/action/replication_record"}},"created_at":"2026-08-07T01:41:29.120204+00:00","updated_at":"2026-08-07T01:41:29.120204+00:00"}