{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T06:49:37Z","timestamp":1685083777556},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T00:00:00Z","timestamp":1522195200000},"content-version":"unspecified","delay-in-days":27,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>\nWe consider the Bernoulli bandit problem where one of the arms has win probability \u03b1 and the others \u03b2, with the identity of the \u03b1 arm specified by initial probabilities. With <jats:italic>u<\/jats:italic> = max(\u03b1, \u03b2), <jats:italic>v<\/jats:italic> = min(\u03b1, \u03b2), call an arm with win probability <jats:italic>u<\/jats:italic> a good arm. Whereas it is known that the strategy of always playing the arm with the largest probability of being a good arm maximizes the expected number of wins in the first <jats:italic>n<\/jats:italic> games for all <jats:italic>n<\/jats:italic>, we conjecture that it also stochastically maximizes the number of wins. That is, we conjecture that this strategy maximizes the probability of at least <jats:italic>k<\/jats:italic> wins in the first <jats:italic>n<\/jats:italic> games for all <jats:italic>k<\/jats:italic>, <jats:italic>n<\/jats:italic>. The conjecture is proven when <jats:italic>k<\/jats:italic> = 1, and <jats:italic>k<\/jats:italic> = <jats:italic>n<\/jats:italic>, and when there are only two arms and <jats:italic>k<\/jats:italic> = <jats:italic>n<\/jats:italic> - 1.\n<\/jats:p>","DOI":"10.1017\/jpr.2018.19","type":"journal-article","created":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T08:20:44Z","timestamp":1522225244000},"page":"318-324","source":"Crossref","is-referenced-by-count":1,"title":["A conjecture on the Feldman bandit problem"],"prefix":"10.1017","volume":"55","author":[{"given":"Maher","family":"Nouiehed","sequence":"first","affiliation":[]},{"given":"Sheldon M.","family":"Ross","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,3,28]]},"reference":[{"key":"S0021900218000190_ref3","volume-title":"Sequential Control With Incomplete Information: The Bayesian Approach to Multi-Armed Bandit Problems","author":"Presman","year":"1990"},{"key":"S0021900218000190_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704454"},{"key":"S0021900218000190_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995533"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900218000190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T19:35:18Z","timestamp":1555356918000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900218000190\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["S0021900218000190"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2018.19","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3]]}}}