{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XVNA6HDFOS4RA2U7FLLVDBQCJA","short_pith_number":"pith:XVNA6HDF","schema_version":"1.0","canonical_sha256":"bd5a0f1c6574b9106a9f2ad75186024835dfc4482f4dbbde1f20ad6f2ec7234d","source":{"kind":"arxiv","id":"2606.06486","version":1},"attestation_state":"computed","paper":{"title":"Regret Minimization with Adaptive Opponents in Repeated Games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.GT"],"primary_cat":"cs.LG","authors_text":"Asuman Ozdaglar, Kaiqing Zhang, Mingyang Liu, Tiancheng Yu","submitted_at":"2026-06-04T17:59:08Z","abstract_excerpt":"In this paper, we study regret minimization in repeated games with \\emph{adaptive} opponents who can respond based on histories of play. The standard metric of \\emph{external regret} in online learning is known to fail to capture such adaptivity. To account for players' counterfactual reasoning, we introduce {\\tt Repeated Policy Regret (RP-Regret)}, a game-theoretic metric that measures the difference between the \\emph{realized} and the \\emph{best-in-hindsight} accumulated utility when all players can \\emph{respond} to the history of play. Compared to existing regret notions in this setting, o"},"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":"2606.06486","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T17:59:08Z","cross_cats_sorted":["cs.AI","cs.GT"],"title_canon_sha256":"9fe5d56c5d2d53d176d6654590a8e09bd46b78c78815d313a1923a972f00bafd","abstract_canon_sha256":"93c1bbffece81fa19b759e73b12aa2ec55cb685c572e1e35c31780fd6734439f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:46.951853Z","signature_b64":"6DbrcnodSUKnlFEUr7tre6lHr5dtUo+Bo5AAs4sS7KBjy1B7kScegM7WVNOGvyXejgi/ZeSZxP8TQ6feQcahDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd5a0f1c6574b9106a9f2ad75186024835dfc4482f4dbbde1f20ad6f2ec7234d","last_reissued_at":"2026-06-05T01:15:46.951454Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:46.951454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regret Minimization with Adaptive Opponents in Repeated Games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.GT"],"primary_cat":"cs.LG","authors_text":"Asuman Ozdaglar, Kaiqing Zhang, Mingyang Liu, Tiancheng Yu","submitted_at":"2026-06-04T17:59:08Z","abstract_excerpt":"In this paper, we study regret minimization in repeated games with \\emph{adaptive} opponents who can respond based on histories of play. The standard metric of \\emph{external regret} in online learning is known to fail to capture such adaptivity. To account for players' counterfactual reasoning, we introduce {\\tt Repeated Policy Regret (RP-Regret)}, a game-theoretic metric that measures the difference between the \\emph{realized} and the \\emph{best-in-hindsight} accumulated utility when all players can \\emph{respond} to the history of play. Compared to existing regret notions in this setting, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06486","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/2606.06486/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":"2606.06486","created_at":"2026-06-05T01:15:46.951519+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06486v1","created_at":"2026-06-05T01:15:46.951519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06486","created_at":"2026-06-05T01:15:46.951519+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVNA6HDFOS4R","created_at":"2026-06-05T01:15:46.951519+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVNA6HDFOS4RA2U7","created_at":"2026-06-05T01:15:46.951519+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVNA6HDF","created_at":"2026-06-05T01:15:46.951519+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA","json":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA.json","graph_json":"https://pith.science/api/pith-number/XVNA6HDFOS4RA2U7FLLVDBQCJA/graph.json","events_json":"https://pith.science/api/pith-number/XVNA6HDFOS4RA2U7FLLVDBQCJA/events.json","paper":"https://pith.science/paper/XVNA6HDF"},"agent_actions":{"view_html":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA","download_json":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA.json","view_paper":"https://pith.science/paper/XVNA6HDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06486&json=true","fetch_graph":"https://pith.science/api/pith-number/XVNA6HDFOS4RA2U7FLLVDBQCJA/graph.json","fetch_events":"https://pith.science/api/pith-number/XVNA6HDFOS4RA2U7FLLVDBQCJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA/action/storage_attestation","attest_author":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA/action/author_attestation","sign_citation":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA/action/citation_signature","submit_replication":"https://pith.science/pith/XVNA6HDFOS4RA2U7FLLVDBQCJA/action/replication_record"}},"created_at":"2026-06-05T01:15:46.951519+00:00","updated_at":"2026-06-05T01:15:46.951519+00:00"}