{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:365KAQLB3HCNYTLWYXOMZO652J","short_pith_number":"pith:365KAQLB","schema_version":"1.0","canonical_sha256":"dfbaa04161d9c4dc4d76c5dcccbbddd273cba8760b98b3cf70ecf97e20488da8","source":{"kind":"arxiv","id":"1511.02176","version":1},"attestation_state":"computed","paper":{"title":"Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"David Pal, Francesco Orabona","submitted_at":"2015-11-06T18:01:38Z","abstract_excerpt":"We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice."},"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":"1511.02176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-06T18:01:38Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"228409fa2b8832f9aee3416bcdacf3dec267a05cb6c689ba3d7f6a4a4953bde1","abstract_canon_sha256":"9aea93a8731ff0ec7f5f6130e7b5b09edc71c4ed9104787cd852afe757d5bf1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:37.571029Z","signature_b64":"Od/pzYUku5VDwZbrPu8Xlqgr+V6E+Njip1A5lOIiSedSjt4BNC3RcosKNDxM7zOkGbHUKMTpdHqYDbE14ouDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfbaa04161d9c4dc4d76c5dcccbbddd273cba8760b98b3cf70ecf97e20488da8","last_reissued_at":"2026-05-18T01:27:37.570302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:37.570302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"David Pal, Francesco Orabona","submitted_at":"2015-11-06T18:01:38Z","abstract_excerpt":"We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02176","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.02176","created_at":"2026-05-18T01:27:37.570429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02176v1","created_at":"2026-05-18T01:27:37.570429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02176","created_at":"2026-05-18T01:27:37.570429+00:00"},{"alias_kind":"pith_short_12","alias_value":"365KAQLB3HCN","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"365KAQLB3HCNYTLW","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"365KAQLB","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J","json":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J.json","graph_json":"https://pith.science/api/pith-number/365KAQLB3HCNYTLWYXOMZO652J/graph.json","events_json":"https://pith.science/api/pith-number/365KAQLB3HCNYTLWYXOMZO652J/events.json","paper":"https://pith.science/paper/365KAQLB"},"agent_actions":{"view_html":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J","download_json":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J.json","view_paper":"https://pith.science/paper/365KAQLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02176&json=true","fetch_graph":"https://pith.science/api/pith-number/365KAQLB3HCNYTLWYXOMZO652J/graph.json","fetch_events":"https://pith.science/api/pith-number/365KAQLB3HCNYTLWYXOMZO652J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J/action/storage_attestation","attest_author":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J/action/author_attestation","sign_citation":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J/action/citation_signature","submit_replication":"https://pith.science/pith/365KAQLB3HCNYTLWYXOMZO652J/action/replication_record"}},"created_at":"2026-05-18T01:27:37.570429+00:00","updated_at":"2026-05-18T01:27:37.570429+00:00"}