{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:VDFWZDXTO6LJBOZYZ2B3PEMOPU","short_pith_number":"pith:VDFWZDXT","schema_version":"1.0","canonical_sha256":"a8cb6c8ef3779690bb38ce83b7918e7d156372162156a328d6c2356fa07d5045","source":{"kind":"arxiv","id":"2311.00676","version":2},"attestation_state":"computed","paper":{"title":"Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.GT","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","submitted_at":"2023-11-01T17:34:58Z","abstract_excerpt":"We study last-iterate convergence properties of algorithms for solving two-player zero-sum games based on Regret Matching$^+$ (RM$^+$). Despite their widespread use for solving real games, virtually nothing is known about their last-iterate convergence. A major obstacle to analyzing RM-type dynamics is that their regret operators lack Lipschitzness and (pseudo)monotonicity. We start by showing numerically that several variants used in practice, such as RM$^+$, predictive RM$^+$ and alternating RM$^+$, all lack last-iterate convergence guarantees even on a simple $3\\times 3$ matrix game. We the"},"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":"2311.00676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2023-11-01T17:34:58Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"52654388f85f3232bf199e2db9ce01814f6b5dc6d3a6fdb297f3e191d3ee5f12","abstract_canon_sha256":"ff726bd670bdcf6e28ad69874798b0e980258bb4aec203a68c66ae6f35dca865"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:23:51.142397Z","signature_b64":"1sqj9yJZGLU7a2eRQ4BjdJL6rMA95lgABi1NSS7B4XYh7AnCfhyCSzC+O0Lto6d+j1zvG7slmT0PmnY4papRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8cb6c8ef3779690bb38ce83b7918e7d156372162156a328d6c2356fa07d5045","last_reissued_at":"2026-07-05T10:23:51.141894Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:23:51.141894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.GT","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","submitted_at":"2023-11-01T17:34:58Z","abstract_excerpt":"We study last-iterate convergence properties of algorithms for solving two-player zero-sum games based on Regret Matching$^+$ (RM$^+$). Despite their widespread use for solving real games, virtually nothing is known about their last-iterate convergence. A major obstacle to analyzing RM-type dynamics is that their regret operators lack Lipschitzness and (pseudo)monotonicity. We start by showing numerically that several variants used in practice, such as RM$^+$, predictive RM$^+$ and alternating RM$^+$, all lack last-iterate convergence guarantees even on a simple $3\\times 3$ matrix game. We the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00676","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/2311.00676/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":"2311.00676","created_at":"2026-07-05T10:23:51.141961+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.00676v2","created_at":"2026-07-05T10:23:51.141961+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00676","created_at":"2026-07-05T10:23:51.141961+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDFWZDXTO6LJ","created_at":"2026-07-05T10:23:51.141961+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDFWZDXTO6LJBOZY","created_at":"2026-07-05T10:23:51.141961+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDFWZDXT","created_at":"2026-07-05T10:23:51.141961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00533","citing_title":"Rapid Learning in Constrained Minimax Games with Negative Momentum","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU","json":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU.json","graph_json":"https://pith.science/api/pith-number/VDFWZDXTO6LJBOZYZ2B3PEMOPU/graph.json","events_json":"https://pith.science/api/pith-number/VDFWZDXTO6LJBOZYZ2B3PEMOPU/events.json","paper":"https://pith.science/paper/VDFWZDXT"},"agent_actions":{"view_html":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU","download_json":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU.json","view_paper":"https://pith.science/paper/VDFWZDXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.00676&json=true","fetch_graph":"https://pith.science/api/pith-number/VDFWZDXTO6LJBOZYZ2B3PEMOPU/graph.json","fetch_events":"https://pith.science/api/pith-number/VDFWZDXTO6LJBOZYZ2B3PEMOPU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU/action/storage_attestation","attest_author":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU/action/author_attestation","sign_citation":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU/action/citation_signature","submit_replication":"https://pith.science/pith/VDFWZDXTO6LJBOZYZ2B3PEMOPU/action/replication_record"}},"created_at":"2026-07-05T10:23:51.141961+00:00","updated_at":"2026-07-05T10:23:51.141961+00:00"}