{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ICNGDYPFXBQDU4FVVE3FVAGVYV","short_pith_number":"pith:ICNGDYPF","canonical_record":{"source":{"id":"1510.01800","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-07T01:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"4c0924e1c90c90e987f3fda75a55fd64f2272577b458ce7098ed19eaca8cc4e9","abstract_canon_sha256":"9dc2fbd85c57b38f4aae1d188d3268c8fed8d67a8f6858402449b6e916fdf453"},"schema_version":"1.0"},"canonical_sha256":"409a61e1e5b8603a70b5a9365a80d5c572bed2b294c2663564d6d4a7301a626b","source":{"kind":"arxiv","id":"1510.01800","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01800","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01800v4","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01800","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"ICNGDYPFXBQD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ICNGDYPFXBQDU4FV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ICNGDYPF","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ICNGDYPFXBQDU4FVVE3FVAGVYV","target":"record","payload":{"canonical_record":{"source":{"id":"1510.01800","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-07T01:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"4c0924e1c90c90e987f3fda75a55fd64f2272577b458ce7098ed19eaca8cc4e9","abstract_canon_sha256":"9dc2fbd85c57b38f4aae1d188d3268c8fed8d67a8f6858402449b6e916fdf453"},"schema_version":"1.0"},"canonical_sha256":"409a61e1e5b8603a70b5a9365a80d5c572bed2b294c2663564d6d4a7301a626b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:43.141338Z","signature_b64":"SLD8WXH5//ZSE6yhjylWA//0NE12NGdbvmpnyU0XxR+vJBU1xyQ1u0fz1ho0wQUn2pasoqDl3GzkYAHDptsfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"409a61e1e5b8603a70b5a9365a80d5c572bed2b294c2663564d6d4a7301a626b","last_reissued_at":"2026-05-18T00:46:43.140820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:43.140820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.01800","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4o7PVDu8bSwYE8qRyilgK+sr9I5y66Nq4oTjjsFPF/GDPMytVd0w1jp4O8JO6nz9EAcmtISDsoZkexEU/veCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T02:32:52.321253Z"},"content_sha256":"1df2cbc32279a4baae8774df4ced6cf98a09b97a5eea8d1a62bc644d53c3de81","schema_version":"1.0","event_id":"sha256:1df2cbc32279a4baae8774df4ced6cf98a09b97a5eea8d1a62bc644d53c3de81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ICNGDYPFXBQDU4FVVE3FVAGVYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic regret bounds for Bandits with Knapsacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arthur Flajolet, Patrick Jaillet","submitted_at":"2015-10-07T01:47:48Z","abstract_excerpt":"Optimal regret bounds for Multi-Armed Bandit problems are now well documented. They can be classified into two categories based on the growth rate with respect to the time horizon $T$: (i) small, distribution-dependent, bounds of order of magnitude $\\ln(T)$ and (ii) robust, distribution-free, bounds of order of magnitude $\\sqrt{T}$. The Bandits with Knapsacks model, an extension to the framework allowing to model resource consumption, lacks this clear-cut distinction. While several algorithms have been shown to achieve asymptotically optimal distribution-free bounds on regret, there has been l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01800","kind":"arxiv","version":4},"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":"2026-05-18T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4J/zQV8DKNPg6fOb1gNcxM9WWkGDSeWNkpyaMF34j7bJ+VWSwAdxpfAcnxBby2gz51c0f/a2lpbH8v7Ulq70CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T02:32:52.321616Z"},"content_sha256":"2be6b59e0fd4bfdeeeaf6dcaaee29345bf94b831bf767308c72fcbfd41c2e48c","schema_version":"1.0","event_id":"sha256:2be6b59e0fd4bfdeeeaf6dcaaee29345bf94b831bf767308c72fcbfd41c2e48c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/bundle.json","state_url":"https://pith.science/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/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":"2026-06-25T02:32:52Z","links":{"resolver":"https://pith.science/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV","bundle":"https://pith.science/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/bundle.json","state":"https://pith.science/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICNGDYPFXBQDU4FVVE3FVAGVYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ICNGDYPFXBQDU4FVVE3FVAGVYV","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":"9dc2fbd85c57b38f4aae1d188d3268c8fed8d67a8f6858402449b6e916fdf453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-07T01:47:48Z","title_canon_sha256":"4c0924e1c90c90e987f3fda75a55fd64f2272577b458ce7098ed19eaca8cc4e9"},"schema_version":"1.0","source":{"id":"1510.01800","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01800","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01800v4","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01800","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"ICNGDYPFXBQD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ICNGDYPFXBQDU4FV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ICNGDYPF","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:2be6b59e0fd4bfdeeeaf6dcaaee29345bf94b831bf767308c72fcbfd41c2e48c","target":"graph","created_at":"2026-05-18T00:46:43Z","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":"Optimal regret bounds for Multi-Armed Bandit problems are now well documented. They can be classified into two categories based on the growth rate with respect to the time horizon $T$: (i) small, distribution-dependent, bounds of order of magnitude $\\ln(T)$ and (ii) robust, distribution-free, bounds of order of magnitude $\\sqrt{T}$. The Bandits with Knapsacks model, an extension to the framework allowing to model resource consumption, lacks this clear-cut distinction. While several algorithms have been shown to achieve asymptotically optimal distribution-free bounds on regret, there has been l","authors_text":"Arthur Flajolet, Patrick Jaillet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-07T01:47:48Z","title":"Logarithmic regret bounds for Bandits with Knapsacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01800","kind":"arxiv","version":4},"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":"sha256:1df2cbc32279a4baae8774df4ced6cf98a09b97a5eea8d1a62bc644d53c3de81","target":"record","created_at":"2026-05-18T00:46:43Z","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":"9dc2fbd85c57b38f4aae1d188d3268c8fed8d67a8f6858402449b6e916fdf453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-07T01:47:48Z","title_canon_sha256":"4c0924e1c90c90e987f3fda75a55fd64f2272577b458ce7098ed19eaca8cc4e9"},"schema_version":"1.0","source":{"id":"1510.01800","kind":"arxiv","version":4}},"canonical_sha256":"409a61e1e5b8603a70b5a9365a80d5c572bed2b294c2663564d6d4a7301a626b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"409a61e1e5b8603a70b5a9365a80d5c572bed2b294c2663564d6d4a7301a626b","first_computed_at":"2026-05-18T00:46:43.140820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:43.140820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLD8WXH5//ZSE6yhjylWA//0NE12NGdbvmpnyU0XxR+vJBU1xyQ1u0fz1ho0wQUn2pasoqDl3GzkYAHDptsfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:43.141338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01800","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1df2cbc32279a4baae8774df4ced6cf98a09b97a5eea8d1a62bc644d53c3de81","sha256:2be6b59e0fd4bfdeeeaf6dcaaee29345bf94b831bf767308c72fcbfd41c2e48c"],"state_sha256":"8c5b77394ce279502a7c51363b5c35ea81663840e7a5a972a76d8c859509ead6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2L/FxwWWnmrQ8co1XvwUacyWrpj01jxXG5twTkjCDrZXLSuzdaFILsKD0lBLVWEQfIjlMN+SzJ0m3WU7BsHcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T02:32:52.323435Z","bundle_sha256":"d518face60baa8532a25ade1eb9088c33ffea9fea8d392f0d772438d2ca93add"}}