{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OUVCBNIQAWI2OIEIOZQDRXEAWD","short_pith_number":"pith:OUVCBNIQ","schema_version":"1.0","canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","source":{"kind":"arxiv","id":"2503.02825","version":1},"attestation_state":"computed","paper":{"title":"On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.OC"],"primary_cat":"cs.LG","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","submitted_at":"2025-03-04T17:49:24Z","abstract_excerpt":"Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow last-iterate convergence even in simple $2 \\times 2$ matrix games, despite many of these dynamics being known to converge asymptotically in the last iterate. It remains unclear, however, whether these algorithms achieve fast non-ergodic convergence under weaker criteria, such as best-iterate conv"},"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":"2503.02825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"e96efa26ff507e8a6822f914f775b398c0b6dda66141844bc4337cc751e94f56","abstract_canon_sha256":"f74d06667c94ddab8a4810fd519fc21b48525e1ad8f2e6628771e63a5c1e1f0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:14.676846Z","signature_b64":"ZQCubs18aDXFhjWhbL7Y0ahzTkkhe+yYY/Z3r25wH3uQLQsOL68fwvmI8eTpkMsFH8TI2RY/f4LpuoNf/e78Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","last_reissued_at":"2026-07-05T10:24:14.676300Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:14.676300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.OC"],"primary_cat":"cs.LG","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","submitted_at":"2025-03-04T17:49:24Z","abstract_excerpt":"Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow last-iterate convergence even in simple $2 \\times 2$ matrix games, despite many of these dynamics being known to converge asymptotically in the last iterate. It remains unclear, however, whether these algorithms achieve fast non-ergodic convergence under weaker criteria, such as best-iterate conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02825","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.02825/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.02825","created_at":"2026-07-05T10:24:14.676370+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.02825v1","created_at":"2026-07-05T10:24:14.676370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02825","created_at":"2026-07-05T10:24:14.676370+00:00"},{"alias_kind":"pith_short_12","alias_value":"OUVCBNIQAWI2","created_at":"2026-07-05T10:24:14.676370+00:00"},{"alias_kind":"pith_short_16","alias_value":"OUVCBNIQAWI2OIEI","created_at":"2026-07-05T10:24:14.676370+00:00"},{"alias_kind":"pith_short_8","alias_value":"OUVCBNIQ","created_at":"2026-07-05T10:24:14.676370+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.12753","citing_title":"Decentralized Multi-Player Q-Learning in Episodic Markov Decision Processes with Information Asymmetry","ref_index":56,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD","json":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD.json","graph_json":"https://pith.science/api/pith-number/OUVCBNIQAWI2OIEIOZQDRXEAWD/graph.json","events_json":"https://pith.science/api/pith-number/OUVCBNIQAWI2OIEIOZQDRXEAWD/events.json","paper":"https://pith.science/paper/OUVCBNIQ"},"agent_actions":{"view_html":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD","download_json":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD.json","view_paper":"https://pith.science/paper/OUVCBNIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.02825&json=true","fetch_graph":"https://pith.science/api/pith-number/OUVCBNIQAWI2OIEIOZQDRXEAWD/graph.json","fetch_events":"https://pith.science/api/pith-number/OUVCBNIQAWI2OIEIOZQDRXEAWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/action/storage_attestation","attest_author":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/action/author_attestation","sign_citation":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/action/citation_signature","submit_replication":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/action/replication_record"}},"created_at":"2026-07-05T10:24:14.676370+00:00","updated_at":"2026-07-05T10:24:14.676370+00:00"}