{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OQXYG5RLJ7UG2ARDWVVXHLHTXT","short_pith_number":"pith:OQXYG5RL","schema_version":"1.0","canonical_sha256":"742f83762b4fe86d0223b56b73acf3bcfcf7955586e7b0197f64574eae7095b4","source":{"kind":"arxiv","id":"1612.02516","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Primal-Dual Methods and Sample Complexity of Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"stat.ML","authors_text":"Mengdi Wang, Yichen Chen","submitted_at":"2016-12-08T03:05:41Z","abstract_excerpt":"We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is observed. These methods use small storage and has low computational complexity per iteration. The SPD methods find an absolute-$\\epsilon$-optimal policy, with high probability, using $\\mathcal{O}\\left(\\frac{|\\mathcal{S}|^4 |\\mathcal{A}|^2\\sigma^2 }{(1-\\gamma)^6\\epsilon^2} \\right)$ i"},"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":"1612.02516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-08T03:05:41Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"62f97b952d4be531bcd8f27d1bd94b6ef287489aa2afde83f51c9c5825dbe19c","abstract_canon_sha256":"23943e0fe3ca6b0bff5e9da6bdd4c0b5f3a61d93fad8ae0432947fb6f5135a77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:33.519865Z","signature_b64":"Q0HM29Rp0H4N9/oi5v7vmV8DFBRdncjLd+trZa9YnqtCMiiNazI7AiuiBlnmiQzBL6wT7kY/ST/BKytvAGXGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"742f83762b4fe86d0223b56b73acf3bcfcf7955586e7b0197f64574eae7095b4","last_reissued_at":"2026-05-18T00:55:33.519167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:33.519167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Primal-Dual Methods and Sample Complexity of Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"stat.ML","authors_text":"Mengdi Wang, Yichen Chen","submitted_at":"2016-12-08T03:05:41Z","abstract_excerpt":"We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is observed. These methods use small storage and has low computational complexity per iteration. The SPD methods find an absolute-$\\epsilon$-optimal policy, with high probability, using $\\mathcal{O}\\left(\\frac{|\\mathcal{S}|^4 |\\mathcal{A}|^2\\sigma^2 }{(1-\\gamma)^6\\epsilon^2} \\right)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02516","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":"1612.02516","created_at":"2026-05-18T00:55:33.519278+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.02516v1","created_at":"2026-05-18T00:55:33.519278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02516","created_at":"2026-05-18T00:55:33.519278+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQXYG5RLJ7UG","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQXYG5RLJ7UG2ARD","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQXYG5RL","created_at":"2026-05-18T12:30:36.002864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2005.01643","citing_title":"Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems","ref_index":281,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06039","citing_title":"Value Mirror Descent for Reinforcement Learning","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT","json":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT.json","graph_json":"https://pith.science/api/pith-number/OQXYG5RLJ7UG2ARDWVVXHLHTXT/graph.json","events_json":"https://pith.science/api/pith-number/OQXYG5RLJ7UG2ARDWVVXHLHTXT/events.json","paper":"https://pith.science/paper/OQXYG5RL"},"agent_actions":{"view_html":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT","download_json":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT.json","view_paper":"https://pith.science/paper/OQXYG5RL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.02516&json=true","fetch_graph":"https://pith.science/api/pith-number/OQXYG5RLJ7UG2ARDWVVXHLHTXT/graph.json","fetch_events":"https://pith.science/api/pith-number/OQXYG5RLJ7UG2ARDWVVXHLHTXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT/action/storage_attestation","attest_author":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT/action/author_attestation","sign_citation":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT/action/citation_signature","submit_replication":"https://pith.science/pith/OQXYG5RLJ7UG2ARDWVVXHLHTXT/action/replication_record"}},"created_at":"2026-05-18T00:55:33.519278+00:00","updated_at":"2026-05-18T00:55:33.519278+00:00"}