The stochastic multiarmed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper, we examine the bandit problem under the weaker assumption that the distributions have moments of order 1 + \u03b5, for some \u03b5 \u2208 (0,1]. Surprisingly, moments of order 2 (i.e., finite variance) are sufficient to obtain regret bounds of the same order as under sub-Gaussian reward distributions. In order to achieve such regret, we define sampling strategies based on refined estimators of the mean such as the truncated empirical mean, Catoni’s M-estimator, and the median-of-means estimator. We also derive matching lower bounds that also show that the best achievable regret deteriorates when \u03b5 <; 1.<\/p>\n","protected":false},"excerpt":{"rendered":"
The stochastic multiarmed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper, we examine the bandit problem under the weaker assumption that the distributions have moments of order 1 + \u03b5, for some \u03b5 \u2208 (0,1]. Surprisingly, moments of order 2 (i.e., finite variance) are sufficient to obtain regret bounds […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"sebubeck","user_id":33570},{"type":"text","value":"Nicol\u00f2 Cesa-Bianchi","user_id":0},{"type":"text","value":"G\u00e1bor Lugosi","user_id":0}],"msr_publishername":"IEEE","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"11","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"7711\u20137717","msr_page_range_start":"7711","msr_page_range_end":"7717","msr_series":"","msr_volume":"59","msr_copyright":"","msr_conference_name":"IEEE Transactions On Information 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