{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:JKQ7M2XRSNKILUNHG2ITG4ADJD","short_pith_number":"pith:JKQ7M2XR","canonical_record":{"source":{"id":"2007.07461","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-15T03:25:24Z","cross_cats_sorted":["cs.GT","cs.MA","math.OC","stat.ML"],"title_canon_sha256":"8d1d4917d70546c77b5495c14893e07b7e5e8a8fa1d4bd7a428289135c9d16e8","abstract_canon_sha256":"7dd1f899b7cfe41602512440830a65414d99a3af94bcd004becf5d631cdbfbb4"},"schema_version":"1.0"},"canonical_sha256":"4aa1f66af1935485d1a7369133700348cadde1924c056f06f9cc51dc647b4eb4","source":{"kind":"arxiv","id":"2007.07461","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.07461","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"2007.07461v3","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.07461","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"JKQ7M2XRSNKI","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_16","alias_value":"JKQ7M2XRSNKILUNH","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_8","alias_value":"JKQ7M2XR","created_at":"2026-07-05T06:39:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:JKQ7M2XRSNKILUNHG2ITG4ADJD","target":"record","payload":{"canonical_record":{"source":{"id":"2007.07461","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-15T03:25:24Z","cross_cats_sorted":["cs.GT","cs.MA","math.OC","stat.ML"],"title_canon_sha256":"8d1d4917d70546c77b5495c14893e07b7e5e8a8fa1d4bd7a428289135c9d16e8","abstract_canon_sha256":"7dd1f899b7cfe41602512440830a65414d99a3af94bcd004becf5d631cdbfbb4"},"schema_version":"1.0"},"canonical_sha256":"4aa1f66af1935485d1a7369133700348cadde1924c056f06f9cc51dc647b4eb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:39:28.341656Z","signature_b64":"4KVRn/3toZaWAi9fGHKHkbjKzxw7Ij6AW55Nf2RpMUVNZ7M6tcokkFEkuu6EZNnW3UEjIlspURS/E1G1LLb8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aa1f66af1935485d1a7369133700348cadde1924c056f06f9cc51dc647b4eb4","last_reissued_at":"2026-07-05T06:39:28.341140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:39:28.341140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.07461","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fO5FkAy5dYN2jIy15eTmqTO07QTj8VtyaE+Mnl34cdgH0Idjj/QDzk6sJIeLg5a5ccGfmEajHpY/Btwoh1BODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:20:57.175790Z"},"content_sha256":"d445c2460d126a34f9e3c7688e511cee1d65beb8059b36703b40a1b04dc59719","schema_version":"1.0","event_id":"sha256:d445c2460d126a34f9e3c7688e511cee1d65beb8059b36703b40a1b04dc59719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:JKQ7M2XRSNKILUNHG2ITG4ADJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","cs.MA","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Kaiqing Zhang, Lin F. Yang, Sham M. Kakade, Tamer Ba\\c{s}ar","submitted_at":"2020-07-15T03:25:24Z","abstract_excerpt":"Model-based reinforcement learning (RL), which finds an optimal policy using an empirical model, has long been recognized as one of the corner stones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously using samples. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated. In this paper, our goal is to address the fundamental question about its sample complexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.07461","kind":"arxiv","version":3},"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/2007.07461/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":"2026-07-05T06:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AtMA+ApqPZ5/d96oUejjL6VExIGFQUsuMUA46V3NcWgJO6PSrYo/2QsX6VHXbDMHGnscuk/qTYPEOe0WivNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:20:57.176542Z"},"content_sha256":"ff81eba1deaf608402250b148390dc9c1f4f3170db39dd46b00e3219d72fb805","schema_version":"1.0","event_id":"sha256:ff81eba1deaf608402250b148390dc9c1f4f3170db39dd46b00e3219d72fb805"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/bundle.json","state_url":"https://pith.science/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/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":"2026-08-11T10:20:57Z","links":{"resolver":"https://pith.science/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD","bundle":"https://pith.science/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/bundle.json","state":"https://pith.science/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKQ7M2XRSNKILUNHG2ITG4ADJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:JKQ7M2XRSNKILUNHG2ITG4ADJD","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":"7dd1f899b7cfe41602512440830a65414d99a3af94bcd004becf5d631cdbfbb4","cross_cats_sorted":["cs.GT","cs.MA","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-15T03:25:24Z","title_canon_sha256":"8d1d4917d70546c77b5495c14893e07b7e5e8a8fa1d4bd7a428289135c9d16e8"},"schema_version":"1.0","source":{"id":"2007.07461","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.07461","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"2007.07461v3","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.07461","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"JKQ7M2XRSNKI","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_16","alias_value":"JKQ7M2XRSNKILUNH","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_8","alias_value":"JKQ7M2XR","created_at":"2026-07-05T06:39:28Z"}],"graph_snapshots":[{"event_id":"sha256:ff81eba1deaf608402250b148390dc9c1f4f3170db39dd46b00e3219d72fb805","target":"graph","created_at":"2026-07-05T06:39:28Z","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/2007.07461/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Model-based reinforcement learning (RL), which finds an optimal policy using an empirical model, has long been recognized as one of the corner stones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously using samples. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated. In this paper, our goal is to address the fundamental question about its sample complexity.","authors_text":"Kaiqing Zhang, Lin F. Yang, Sham M. Kakade, Tamer Ba\\c{s}ar","cross_cats":["cs.GT","cs.MA","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-15T03:25:24Z","title":"Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.07461","kind":"arxiv","version":3},"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:d445c2460d126a34f9e3c7688e511cee1d65beb8059b36703b40a1b04dc59719","target":"record","created_at":"2026-07-05T06:39:28Z","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":"7dd1f899b7cfe41602512440830a65414d99a3af94bcd004becf5d631cdbfbb4","cross_cats_sorted":["cs.GT","cs.MA","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-15T03:25:24Z","title_canon_sha256":"8d1d4917d70546c77b5495c14893e07b7e5e8a8fa1d4bd7a428289135c9d16e8"},"schema_version":"1.0","source":{"id":"2007.07461","kind":"arxiv","version":3}},"canonical_sha256":"4aa1f66af1935485d1a7369133700348cadde1924c056f06f9cc51dc647b4eb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aa1f66af1935485d1a7369133700348cadde1924c056f06f9cc51dc647b4eb4","first_computed_at":"2026-07-05T06:39:28.341140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:39:28.341140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KVRn/3toZaWAi9fGHKHkbjKzxw7Ij6AW55Nf2RpMUVNZ7M6tcokkFEkuu6EZNnW3UEjIlspURS/E1G1LLb8DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:39:28.341656Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.07461","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d445c2460d126a34f9e3c7688e511cee1d65beb8059b36703b40a1b04dc59719","sha256:ff81eba1deaf608402250b148390dc9c1f4f3170db39dd46b00e3219d72fb805"],"state_sha256":"9cac41eb4bd9a812f5da5860c0e5f45f4c9c57a97bf9df963b333214e67cb217"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RirsFneQjzVlPugnSpHL579jswaZa/hIslI9B8fRzYIBUtl2znKrsWlYhUDK2byBCMVYFeyl/80dWck9h55SDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:20:57.185400Z","bundle_sha256":"1f4bae6092f256836284f8cb43932b35c681601620e7f9975611b5541eca4c70"}}