{"paper":{"title":"On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"math.OC","authors_text":"Maryam Kamgarpour, Tatiana Tatarenko","submitted_at":"2022-02-22T19:45:48Z","abstract_excerpt":"We derive the rate of convergence to Nash equilibria for the payoff-based algorithm proposed in \\cite{tat_kam_TAC}. These rates are achieved under the standard assumption of convexity of the game, strong monotonicity and differentiability of the pseudo-gradient. In particular, we show the algorithm achieves $O(\\frac{1}{T})$ in the two-point function evaluating setting and $O(\\frac{1}{\\sqrt{T}})$ in the one-point function evaluation under additional requirement of Lipschitz continuity of the pseudo-gradient. These rates are to our knowledge the best known rates for the corresponding problem cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11147","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/2202.11147/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"}