{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PZK23SLQDZC7YEDJ4W7D64MY5I","short_pith_number":"pith:PZK23SLQ","canonical_record":{"source":{"id":"1803.07617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-20T19:29:46Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"35d493f09315227d36535a2f53d81e73bba63fbbe2a54622779600e2ee5e9356","abstract_canon_sha256":"49badf431234de1b5098fe621317d349574e7fbfda29b422e39a429ad5a6f6b8"},"schema_version":"1.0"},"canonical_sha256":"7e55adc9701e45fc1069e5be3f7198ea091825fabd13549f34c4d47a01377fcf","source":{"kind":"arxiv","id":"1803.07617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07617","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07617v1","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07617","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"PZK23SLQDZC7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PZK23SLQDZC7YEDJ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PZK23SLQ","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PZK23SLQDZC7YEDJ4W7D64MY5I","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-20T19:29:46Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"35d493f09315227d36535a2f53d81e73bba63fbbe2a54622779600e2ee5e9356","abstract_canon_sha256":"49badf431234de1b5098fe621317d349574e7fbfda29b422e39a429ad5a6f6b8"},"schema_version":"1.0"},"canonical_sha256":"7e55adc9701e45fc1069e5be3f7198ea091825fabd13549f34c4d47a01377fcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:29.413205Z","signature_b64":"K2/JHapT/VBpM/QiwLXIungoLuGO6ozhTP9YC9NySZtq+tsTti2m0ajz4EaHtDdXy6JYfr0ZzW3qwpUJqxtAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e55adc9701e45fc1069e5be3f7198ea091825fabd13549f34c4d47a01377fcf","last_reissued_at":"2026-05-18T00:20:29.412659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:29.412659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07617","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rwq3g4sCexHSsPJzo6uxqCpzEn0EXAP0kozoisx518h1ioF67YPXVNrFjljKO/TkTuQyGte19CbE+Wir2XIsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:05:14.453007Z"},"content_sha256":"dc476dfbbed0d9d665b90a02ade48ceeb32125357c2e5304e3abae885eda968c","schema_version":"1.0","event_id":"sha256:dc476dfbbed0d9d665b90a02ade48ceeb32125357c2e5304e3abae885eda968c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PZK23SLQDZC7YEDJ4W7D64MY5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Learning: Sufficient Statistics and the Burkholder Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexander Rakhlin, Dylan J. Foster, Karthik Sridharan","submitted_at":"2018-03-20T19:29:46Z","abstract_excerpt":"We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain \"sufficient statistics\" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is only required to keep the sufficient statistics in memory. This characterization is achieved by bringing the full power of the Burkholder Method --- originally developed for certifying probabilistic mar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07617","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2h2PognmwAb687G/Ai/qfcUTw87dSq9NeW2RXgBigA8qlXouz3ouvSFPmZx/lliS90usgoZDBPq5J8VIcrTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:05:14.453343Z"},"content_sha256":"4ef4e92a1e3fdb9c1993d184f33367e8ebe6598c4cfed62d9011028cfe6089d7","schema_version":"1.0","event_id":"sha256:4ef4e92a1e3fdb9c1993d184f33367e8ebe6598c4cfed62d9011028cfe6089d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/bundle.json","state_url":"https://pith.science/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T08:05:14Z","links":{"resolver":"https://pith.science/pith/PZK23SLQDZC7YEDJ4W7D64MY5I","bundle":"https://pith.science/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/bundle.json","state":"https://pith.science/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZK23SLQDZC7YEDJ4W7D64MY5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PZK23SLQDZC7YEDJ4W7D64MY5I","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"49badf431234de1b5098fe621317d349574e7fbfda29b422e39a429ad5a6f6b8","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-20T19:29:46Z","title_canon_sha256":"35d493f09315227d36535a2f53d81e73bba63fbbe2a54622779600e2ee5e9356"},"schema_version":"1.0","source":{"id":"1803.07617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07617","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07617v1","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07617","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"PZK23SLQDZC7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PZK23SLQDZC7YEDJ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PZK23SLQ","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:4ef4e92a1e3fdb9c1993d184f33367e8ebe6598c4cfed62d9011028cfe6089d7","target":"graph","created_at":"2026-05-18T00:20:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain \"sufficient statistics\" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is only required to keep the sufficient statistics in memory. This characterization is achieved by bringing the full power of the Burkholder Method --- originally developed for certifying probabilistic mar","authors_text":"Alexander Rakhlin, Dylan J. Foster, Karthik Sridharan","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-20T19:29:46Z","title":"Online Learning: Sufficient Statistics and the Burkholder Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07617","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dc476dfbbed0d9d665b90a02ade48ceeb32125357c2e5304e3abae885eda968c","target":"record","created_at":"2026-05-18T00:20:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"49badf431234de1b5098fe621317d349574e7fbfda29b422e39a429ad5a6f6b8","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-20T19:29:46Z","title_canon_sha256":"35d493f09315227d36535a2f53d81e73bba63fbbe2a54622779600e2ee5e9356"},"schema_version":"1.0","source":{"id":"1803.07617","kind":"arxiv","version":1}},"canonical_sha256":"7e55adc9701e45fc1069e5be3f7198ea091825fabd13549f34c4d47a01377fcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e55adc9701e45fc1069e5be3f7198ea091825fabd13549f34c4d47a01377fcf","first_computed_at":"2026-05-18T00:20:29.412659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:29.412659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2/JHapT/VBpM/QiwLXIungoLuGO6ozhTP9YC9NySZtq+tsTti2m0ajz4EaHtDdXy6JYfr0ZzW3qwpUJqxtAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:29.413205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc476dfbbed0d9d665b90a02ade48ceeb32125357c2e5304e3abae885eda968c","sha256:4ef4e92a1e3fdb9c1993d184f33367e8ebe6598c4cfed62d9011028cfe6089d7"],"state_sha256":"ffdcc21fcc5bef09aa1e554cc74b53d6e902426054171f510f70ac6e36971ed1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ng0qvdNLEvoolOUGuiQ3ui3gqCbOvXGElLqm8PwYlp4kmzDf+kECe/S4wEW3I3g02V0BR1LboZTFUEuhNhq5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:05:14.455200Z","bundle_sha256":"a9a9c626ce0e45c4fb849e2a22dea3f4844454a583795c48cf44ccd9cb73d4d9"}}