{"paper":{"title":"Fast Rates in $\\alpha$-Potential Games via Regularized Mirror Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Offline Potential Mirror Descent achieves an accelerated Õ(1/n) rate for learning Nash equilibria in α-potential games.","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Claire Chen, Yuheng Zhang","submitted_at":"2026-04-30T22:04:34Z","abstract_excerpt":"An $\\alpha$-potential game is a multi-player non-cooperative interaction in which a global potential function approximates individual player rewards up to a structural bias $\\alpha$. While identifying a Nash Equilibrium (NE) in generic general-sum games is known to be computationally intractable, the potential game structure enables tractable NE identification. In this paper, we study the offline learning of NE in $\\alpha$-potential games using KL regularization. To analyze this process, we propose a novel Reference-Anchored offline data coverage framework--a verifiable condition that anchors "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"OPMD achieves an accelerated Õ(1/n) statistical rate, surpassing the standard Õ(1/√n) rate typical of offline multi-agent learning, and characterizes the first fast-rate offline learning approach for α-potential games.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The novel Reference-Anchored offline data coverage condition holds and can be verified using a known reference policy rather than the unknown optimum.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"OPMD achieves the first fast Õ(1/n) rate for offline Nash equilibrium learning in α-potential games via a new reference-anchored coverage framework.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Offline Potential Mirror Descent achieves an accelerated Õ(1/n) rate for learning Nash equilibria in α-potential games.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2b7b49907d86c61fe6696e656a2ee5aaab175184c49360d08057335b9f8f58bc"},"source":{"id":"2605.00268","kind":"arxiv","version":2},"verdict":{"id":"b1da5bf0-cb55-4373-9b9d-fa7cd4bdd439","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:24:00.431005Z","strongest_claim":"OPMD achieves an accelerated Õ(1/n) statistical rate, surpassing the standard Õ(1/√n) rate typical of offline multi-agent learning, and characterizes the first fast-rate offline learning approach for α-potential games.","one_line_summary":"OPMD achieves the first fast Õ(1/n) rate for offline Nash equilibrium learning in α-potential games via a new reference-anchored coverage framework.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The novel Reference-Anchored offline data coverage condition holds and can be verified using a known reference policy rather than the unknown optimum.","pith_extraction_headline":"Offline Potential Mirror Descent achieves an accelerated Õ(1/n) rate for learning Nash equilibria in α-potential games."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00268/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:22:29.269561Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d48ea71536116ebe1679e9cb515fe044ee9090d3aea25f05e5bf08fbfe3b8c21"},"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"}