{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T21:59:15Z","timestamp":1763071155663,"version":"3.40.5"},"reference-count":17,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p> This note gives a short, self-contained proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multiarmed bandit problem with discount factor [Formula: see text]. The Gittins index of an arm is shown to equal the [Formula: see text]-quantile of the posterior distribution of the arm's mean plus an error term that vanishes as [Formula: see text]. In this sense, for sufficiently patient agents, a Gittins index measures the highest plausible mean-reward of an arm in a manner equivalent to an upper confidence bound. <\/jats:p>","DOI":"10.1287\/opre.2020.1987","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T19:41:20Z","timestamp":1608838880000},"page":"273-278","source":"Crossref","is-referenced-by-count":5,"title":["Technical Note\u2014A Note on the Equivalence of Upper Confidence Bounds and Gittins Indices for Patient Agents"],"prefix":"10.1287","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5926-8624","authenticated-orcid":false,"given":"Daniel","family":"Russo","sequence":"first","affiliation":[{"name":"Graduate School of Business, Columbia University, New York, New York 10027"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"doi-asserted-by":"publisher","key":"B1","DOI":"10.1023\/A:1013689704352"},{"doi-asserted-by":"publisher","key":"B3","DOI":"10.1017\/S0269964803171045"},{"doi-asserted-by":"publisher","key":"B4","DOI":"10.1214\/13-AOS1119"},{"doi-asserted-by":"publisher","key":"B5","DOI":"10.2307\/1427104"},{"doi-asserted-by":"publisher","key":"B6","DOI":"10.1287\/mnsc.1080.0949"},{"doi-asserted-by":"publisher","key":"B7","DOI":"10.1214\/aoms\/1177704567"},{"doi-asserted-by":"publisher","key":"B9","DOI":"10.1093\/biomet\/66.3.561"},{"doi-asserted-by":"publisher","key":"B10","DOI":"10.1002\/9780470980033"},{"doi-asserted-by":"publisher","key":"B11","DOI":"10.1214\/aoms\/1177731721"},{"unstructured":"Kaufmann E, Capp\u00e9 O, Garivier A (2012) On Bayesian upper confidence bounds for bandit problems. Proc. Conf. Artificial Intelligence Statist. (PLMR, La Palma, Canary Islands), 592\u2013600.","key":"B13"},{"doi-asserted-by":"publisher","key":"B14","DOI":"10.1016\/0196-8858(85)90002-8"},{"unstructured":"Lattimore T (2016) Regret analysis of the finite-horizon Gittins index strategy for multi-armed bandits. Feldman V, Rakhlin A, Shamir O, eds. Proc. Conf. Learn. Theory, (PLMR, New York)1214\u20131245.","key":"B15"},{"doi-asserted-by":"publisher","key":"B16","DOI":"10.1287\/ijoc.1100.0398"},{"doi-asserted-by":"publisher","key":"B18","DOI":"10.1287\/moor.1100.0446"},{"doi-asserted-by":"publisher","key":"B19","DOI":"10.1109\/TIT.2011.2182033"},{"doi-asserted-by":"publisher","key":"B20","DOI":"10.1214\/aoap\/1177005588"},{"doi-asserted-by":"publisher","key":"B21","DOI":"10.1214\/074921706000001111"}],"container-title":["Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/opre.2020.1987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T20:15:52Z","timestamp":1680466552000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/opre.2020.1987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1287\/opre.2020.1987"],"URL":"https:\/\/doi.org\/10.1287\/opre.2020.1987","relation":{},"ISSN":["0030-364X","1526-5463"],"issn-type":[{"type":"print","value":"0030-364X"},{"type":"electronic","value":"1526-5463"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}