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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, ours is native to repeated game playing, enabling stronger comparators and opponents with fewer constraints, while maintaining the possibility of finding better equilibria when all players minimize it. We first identify necessary conditions for obtaining {\\tt RP-Regret} sublinear in time, on the variation of the player's comparator strategies in th","title":"Regret Minimization with Adaptive Opponents in Repeated Games","url":"https://arxiv.org/abs/2606.06486","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.06486v1 Announce Type: cross \nAbstract: 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, ours is native to repeated game playing, enabling stronger comparators and opponents with fewer constraints, while maintaining the possibility of finding better equilibria when all players minimize it. We first identify necessary conditions for obtaining {\\tt RP-Regret} sublinear in time, on the variation of the player's comparator strategies in th","title":"Regret Minimization with Adaptive Opponents in Repeated Games","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-06T04:43:19Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.06486"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:cfa66afa14a6555562c178f1e7a6c4b228d271235649907173d9e75ef0adfe5bb3b5811016536c27df3ab90bb76e99af8588702ea0d30be039d623382de2eb05","signer":"crovia.substrate","subject":{"observed_at":"2026-06-06T04:43:19Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.06486"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"868f8baab5f5ab5442a1ceccd92a1e3b5e23c27d7306ed2b1f0dca4d67e049bb","leaf_index":219415,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"c1ac57dd16a261eb856510d7ad8f34752d3f4d765b4670dc88bd1bd42d103d43","side":"left"},{"sibling":"4093be10b7e12fa9b2b77209d1d5f47616e13c54140143c94b309d079b74934a","side":"left"},{"sibling":"9295477f6d4c152e59c83e2dfa3a44559a704440bd8a9b693a44e647f5e5bcd6","side":"left"},{"sibling":"8b96d682b2d1578db854f4fab0d05dfbef63a489d965b94ee51c44dd1ff295c8","side":"right"},{"sibling":"e3fb5287f34974267078112dd81bf6efd2a537b8a26680980d46730033a57394","side":"left"},{"sibling":"9263347d3689a7d3e52b35ed5a9ab4c610eb624941b2946dbf26fb2b9ed85bc8","side":"right"},{"sibling":"c6d85f421226f83ff8cf32aaff89929d6dc9d5d94759254073631ced17a73907","side":"right"},{"sibling":"242ec7690d5995e1b5c2e94f2a8cedd5416b170d2db6fb44c95d0f9fb134a235","side":"right"},{"sibling":"42875175baa73c49869c927a23711e8bef732331ce49af85fa7e86d0903b1066","side":"left"},{"sibling":"84d2509eab51047589142ed6da8c496305d2fbcbe148e0e6755163db2c7a4bc4","side":"right"},{"sibling":"9e3ea17e834fab022f2eabcfedb8ea0ac95c1f9fb57edc5004dded68522d3c9e","side":"right"},{"sibling":"41d58fea95a95071715ee23ef8bcd15f5867a3639da28e62a0641bc95eb83094","side":"left"},{"sibling":"27ad9d6a9ab792d708709017242a61b9ca519da4e035f87a342811aae221d000","side":"left"},{"sibling":"5f303e2a7840c60038ff2d035b1cd911feefb0fba880de2d737c6671ace594d4","side":"right"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"1a61eadbf0217d063ab78291ccafdc0c92907f7d6ccdc3357534ef89f07d78ae","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":219672,"merkle_root":"d3e32d3a61ca02ce6b1f0b2db86721107770b250e8a5bf762a2c225d2f03c870","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260606T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-06T05:38:35Z","sig_algorithm":"ed25519","signature":"dab214c2d4d857f01383c8e93a521a774b1aba60eaee5677d4e43e4074f0342b2c6a9b9bfcff0eba74f7ac81fcb490dd0e43727979c1a7e8979c7e11547fb101","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_c89b3c97d426f3a4f1f9f7006b7ad48900d8f6b99bbdece4c9c16ad4ce96c867"}}