{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ERVNCQVYW2CIMWVFVOUWBUIINE","short_pith_number":"pith:ERVNCQVY","canonical_record":{"source":{"id":"1906.04697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-11T16:58:54Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"d75338aa06308d84e45cb05abc237c06ddaa5cc00ec9533f84adab92c43af17e","abstract_canon_sha256":"15415d89e4fbf9d6cf6fcb5c681cc28c4df1d48d046a4d7766c52e0e3ba900ff"},"schema_version":"1.0"},"canonical_sha256":"246ad142b8b684865aa5aba960d1086909677731aa0b0cb69322984a4c8e5b56","source":{"kind":"arxiv","id":"1906.04697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04697","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04697v2","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04697","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_12","alias_value":"ERVNCQVYW2CI","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_16","alias_value":"ERVNCQVYW2CIMWVF","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_8","alias_value":"ERVNCQVY","created_at":"2026-07-04T23:52:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ERVNCQVYW2CIMWVFVOUWBUIINE","target":"record","payload":{"canonical_record":{"source":{"id":"1906.04697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-11T16:58:54Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"d75338aa06308d84e45cb05abc237c06ddaa5cc00ec9533f84adab92c43af17e","abstract_canon_sha256":"15415d89e4fbf9d6cf6fcb5c681cc28c4df1d48d046a4d7766c52e0e3ba900ff"},"schema_version":"1.0"},"canonical_sha256":"246ad142b8b684865aa5aba960d1086909677731aa0b0cb69322984a4c8e5b56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:21.687012Z","signature_b64":"6/qhdc+hib6GMn1AO6nQMyJfHj/Z9iixVakOCc+Z20xcu6K0fHsjSbv4/iABkOvFvaEwA581vdE4dqoM7oG6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"246ad142b8b684865aa5aba960d1086909677731aa0b0cb69322984a4c8e5b56","last_reissued_at":"2026-07-04T23:52:21.686510Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:21.686510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.04697","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:52:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upLyzb0ZN3NO29ap6eTEkKeuihGyxwzkjDUUh67kE372Ppp3WvPX8uSMfq5LLfTsTO814r7x/a2kXCYDIlJ/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T02:52:24.297065Z"},"content_sha256":"dceafee18266af78cbbbdcd36e4a10b2c96f74243bf0dab80054573f8a4ca1d4","schema_version":"1.0","event_id":"sha256:dceafee18266af78cbbbdcd36e4a10b2c96f74243bf0dab80054573f8a4ca1d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ERVNCQVYW2CIMWVFVOUWBUIINE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variance-reduced $Q$-learning is minimax optimal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Martin J. Wainwright","submitted_at":"2019-06-11T16:58:54Z","abstract_excerpt":"We introduce and analyze a form of variance-reduced $Q$-learning. For $\\gamma$-discounted MDPs with finite state space $\\mathcal{X}$ and action space $\\mathcal{U}$, we prove that it yields an $\\epsilon$-accurate estimate of the optimal $Q$-function in the $\\ell_\\infty$-norm using $\\mathcal{O} \\left(\\left(\\frac{D}{ \\epsilon^2 (1-\\gamma)^3} \\right) \\; \\log \\left( \\frac{D}{(1-\\gamma)} \\right) \\right)$ samples, where $D = |\\mathcal{X}| \\times |\\mathcal{U}|$. This guarantee matches known minimax lower bounds up to a logarithmic factor in the discount complexity. In contrast, our past work shows tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04697","kind":"arxiv","version":2},"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/1906.04697/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:52:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+O6xZvkLLqZXcASKMrGnKtvvDMSmdeRKKHkeMf/B3YBT2mZQDojx6EvQ3+s6rFAfv+jEX8q++CeT1CtK5BTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T02:52:24.297468Z"},"content_sha256":"631b55c2d063a19d442b5470e8efd68f9e29e23beb5a17206cc955309e9f9534","schema_version":"1.0","event_id":"sha256:631b55c2d063a19d442b5470e8efd68f9e29e23beb5a17206cc955309e9f9534"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/bundle.json","state_url":"https://pith.science/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/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":"2026-07-13T02:52:24Z","links":{"resolver":"https://pith.science/pith/ERVNCQVYW2CIMWVFVOUWBUIINE","bundle":"https://pith.science/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/bundle.json","state":"https://pith.science/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERVNCQVYW2CIMWVFVOUWBUIINE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ERVNCQVYW2CIMWVFVOUWBUIINE","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":"15415d89e4fbf9d6cf6fcb5c681cc28c4df1d48d046a4d7766c52e0e3ba900ff","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-11T16:58:54Z","title_canon_sha256":"d75338aa06308d84e45cb05abc237c06ddaa5cc00ec9533f84adab92c43af17e"},"schema_version":"1.0","source":{"id":"1906.04697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04697","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04697v2","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04697","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_12","alias_value":"ERVNCQVYW2CI","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_16","alias_value":"ERVNCQVYW2CIMWVF","created_at":"2026-07-04T23:52:21Z"},{"alias_kind":"pith_short_8","alias_value":"ERVNCQVY","created_at":"2026-07-04T23:52:21Z"}],"graph_snapshots":[{"event_id":"sha256:631b55c2d063a19d442b5470e8efd68f9e29e23beb5a17206cc955309e9f9534","target":"graph","created_at":"2026-07-04T23:52:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1906.04697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and analyze a form of variance-reduced $Q$-learning. For $\\gamma$-discounted MDPs with finite state space $\\mathcal{X}$ and action space $\\mathcal{U}$, we prove that it yields an $\\epsilon$-accurate estimate of the optimal $Q$-function in the $\\ell_\\infty$-norm using $\\mathcal{O} \\left(\\left(\\frac{D}{ \\epsilon^2 (1-\\gamma)^3} \\right) \\; \\log \\left( \\frac{D}{(1-\\gamma)} \\right) \\right)$ samples, where $D = |\\mathcal{X}| \\times |\\mathcal{U}|$. This guarantee matches known minimax lower bounds up to a logarithmic factor in the discount complexity. In contrast, our past work shows tha","authors_text":"Martin J. Wainwright","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-11T16:58:54Z","title":"Variance-reduced $Q$-learning is minimax optimal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04697","kind":"arxiv","version":2},"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:dceafee18266af78cbbbdcd36e4a10b2c96f74243bf0dab80054573f8a4ca1d4","target":"record","created_at":"2026-07-04T23:52:21Z","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":"15415d89e4fbf9d6cf6fcb5c681cc28c4df1d48d046a4d7766c52e0e3ba900ff","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-11T16:58:54Z","title_canon_sha256":"d75338aa06308d84e45cb05abc237c06ddaa5cc00ec9533f84adab92c43af17e"},"schema_version":"1.0","source":{"id":"1906.04697","kind":"arxiv","version":2}},"canonical_sha256":"246ad142b8b684865aa5aba960d1086909677731aa0b0cb69322984a4c8e5b56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"246ad142b8b684865aa5aba960d1086909677731aa0b0cb69322984a4c8e5b56","first_computed_at":"2026-07-04T23:52:21.686510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:21.686510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/qhdc+hib6GMn1AO6nQMyJfHj/Z9iixVakOCc+Z20xcu6K0fHsjSbv4/iABkOvFvaEwA581vdE4dqoM7oG6BA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:21.687012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dceafee18266af78cbbbdcd36e4a10b2c96f74243bf0dab80054573f8a4ca1d4","sha256:631b55c2d063a19d442b5470e8efd68f9e29e23beb5a17206cc955309e9f9534"],"state_sha256":"492a96baa1dee2a004d01c858a377235400b9c9083af121b38b5b3cda5fbbffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFXmiIXSSHEJYE/P649ATRPscjyCJFMILx+wvlisOvaBQo4t3DbSkCUmxl4qvMtiD3zp9aRAf7/L21KtfejbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T02:52:24.300607Z","bundle_sha256":"0778d6201893ca3a6e794958fac6a747fa7e94a01fb829209971063d4c2a0e6f"}}