{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NIBGPROUIXIU5PXOHC4QZN77BB","short_pith_number":"pith:NIBGPROU","canonical_record":{"source":{"id":"2201.03522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-10T18:34:32Z","cross_cats_sorted":["cs.AI","cs.GT","stat.ML"],"title_canon_sha256":"d515c71ac6a05805a8b4f4b02cca301feaf1e3e26aeacf4a9d2c2df41798a686","abstract_canon_sha256":"237f68da8be2712d4537792335d0bc1d70e8969b7b523319ba40590d7498cde6"},"schema_version":"1.0"},"canonical_sha256":"6a0267c5d445d14ebeee38b90cb7ff087673d3f9a66cb72115d7ca53e19188d5","source":{"kind":"arxiv","id":"2201.03522","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.03522","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"2201.03522v2","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.03522","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"NIBGPROUIXIU","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"NIBGPROUIXIU5PXO","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"NIBGPROU","created_at":"2026-07-05T05:06:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NIBGPROUIXIU5PXOHC4QZN77BB","target":"record","payload":{"canonical_record":{"source":{"id":"2201.03522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-10T18:34:32Z","cross_cats_sorted":["cs.AI","cs.GT","stat.ML"],"title_canon_sha256":"d515c71ac6a05805a8b4f4b02cca301feaf1e3e26aeacf4a9d2c2df41798a686","abstract_canon_sha256":"237f68da8be2712d4537792335d0bc1d70e8969b7b523319ba40590d7498cde6"},"schema_version":"1.0"},"canonical_sha256":"6a0267c5d445d14ebeee38b90cb7ff087673d3f9a66cb72115d7ca53e19188d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:29.278948Z","signature_b64":"uUochQa0KZk4sIhr9BN0aWz9XIWNVs+goo5tRk6GmMe+lATL1AgjtAjZQW2z0SdhdbMkJKYgEcSksv8szLy9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a0267c5d445d14ebeee38b90cb7ff087673d3f9a66cb72115d7ca53e19188d5","last_reissued_at":"2026-07-05T05:06:29.278519Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:29.278519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.03522","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":"2026-07-05T05:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZrgKpjKuQNB1KlbIedzzgPJvRWPZ+Gw3alDOqQf6unuqwBOfpM1zPwyijBEvFRSQTlesX9p4BXgzFMQ58pCNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T21:11:36.758293Z"},"content_sha256":"5faef9a6fef816bd642560c1fd26615e37752f74afd5d441b480c460d3a7ec7e","schema_version":"1.0","event_id":"sha256:5faef9a6fef816bd642560c1fd26615e37752f74afd5d441b480c460d3a7ec7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NIBGPROUIXIU5PXOHC4QZN77BB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When is Offline Two-Player Zero-Sum Markov Game Solvable?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.GT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Qiwen Cui, Simon S. Du","submitted_at":"2022-01-10T18:34:32Z","abstract_excerpt":"We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for learning the Nash equilibrium (NE) strategy in offline two-player zero-sum Markov games. On the other hand, we propose a new assumption named unilateral concentration and design a pessimism-type algorithm that is provably efficient under this assumption. In addition, we show that the unilateral concentration assumption is necessary for learning an NE strateg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03522","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/2201.03522/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":"2026-07-05T05:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPuuR/qMb/BNbwwOAghRTwmWxg5NbK7kXKkj1ywojtWrUDig0cYCeCN86cUp2TQWB2yqAo8F8zSynrLULOyUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T21:11:36.758686Z"},"content_sha256":"34c32263c3c0d11d1d15a4429b29e1477ab29f9f8609203c7aa7d95f787f38d3","schema_version":"1.0","event_id":"sha256:34c32263c3c0d11d1d15a4429b29e1477ab29f9f8609203c7aa7d95f787f38d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIBGPROUIXIU5PXOHC4QZN77BB/bundle.json","state_url":"https://pith.science/pith/NIBGPROUIXIU5PXOHC4QZN77BB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIBGPROUIXIU5PXOHC4QZN77BB/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":"2026-07-12T21:11:36Z","links":{"resolver":"https://pith.science/pith/NIBGPROUIXIU5PXOHC4QZN77BB","bundle":"https://pith.science/pith/NIBGPROUIXIU5PXOHC4QZN77BB/bundle.json","state":"https://pith.science/pith/NIBGPROUIXIU5PXOHC4QZN77BB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIBGPROUIXIU5PXOHC4QZN77BB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NIBGPROUIXIU5PXOHC4QZN77BB","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":"237f68da8be2712d4537792335d0bc1d70e8969b7b523319ba40590d7498cde6","cross_cats_sorted":["cs.AI","cs.GT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-10T18:34:32Z","title_canon_sha256":"d515c71ac6a05805a8b4f4b02cca301feaf1e3e26aeacf4a9d2c2df41798a686"},"schema_version":"1.0","source":{"id":"2201.03522","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.03522","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"2201.03522v2","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.03522","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"NIBGPROUIXIU","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"NIBGPROUIXIU5PXO","created_at":"2026-07-05T05:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"NIBGPROU","created_at":"2026-07-05T05:06:29Z"}],"graph_snapshots":[{"event_id":"sha256:34c32263c3c0d11d1d15a4429b29e1477ab29f9f8609203c7aa7d95f787f38d3","target":"graph","created_at":"2026-07-05T05:06:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.03522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for learning the Nash equilibrium (NE) strategy in offline two-player zero-sum Markov games. On the other hand, we propose a new assumption named unilateral concentration and design a pessimism-type algorithm that is provably efficient under this assumption. In addition, we show that the unilateral concentration assumption is necessary for learning an NE strateg","authors_text":"Qiwen Cui, Simon S. Du","cross_cats":["cs.AI","cs.GT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-10T18:34:32Z","title":"When is Offline Two-Player Zero-Sum Markov Game Solvable?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03522","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":"sha256:5faef9a6fef816bd642560c1fd26615e37752f74afd5d441b480c460d3a7ec7e","target":"record","created_at":"2026-07-05T05:06:29Z","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":"237f68da8be2712d4537792335d0bc1d70e8969b7b523319ba40590d7498cde6","cross_cats_sorted":["cs.AI","cs.GT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-10T18:34:32Z","title_canon_sha256":"d515c71ac6a05805a8b4f4b02cca301feaf1e3e26aeacf4a9d2c2df41798a686"},"schema_version":"1.0","source":{"id":"2201.03522","kind":"arxiv","version":2}},"canonical_sha256":"6a0267c5d445d14ebeee38b90cb7ff087673d3f9a66cb72115d7ca53e19188d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a0267c5d445d14ebeee38b90cb7ff087673d3f9a66cb72115d7ca53e19188d5","first_computed_at":"2026-07-05T05:06:29.278519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:29.278519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUochQa0KZk4sIhr9BN0aWz9XIWNVs+goo5tRk6GmMe+lATL1AgjtAjZQW2z0SdhdbMkJKYgEcSksv8szLy9Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:29.278948Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.03522","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5faef9a6fef816bd642560c1fd26615e37752f74afd5d441b480c460d3a7ec7e","sha256:34c32263c3c0d11d1d15a4429b29e1477ab29f9f8609203c7aa7d95f787f38d3"],"state_sha256":"8762d60d1a0f6133e0b9b97ecc4ed71e0029edfd8c48476ad3f030ba2a499123"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NN5yJx6qtuqVVjUzt+TVDUHU/dQ8codC0RdP/RiUIFwrgyrR5Rr71v0ZcwRYemQHJ5lzJND2KPnhdRiZJIuiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T21:11:36.761167Z","bundle_sha256":"287646a16342c0cc3abf655308000df97c9a073de98bc224a1c5c89361a412ab"}}