{"id":2308,"date":"2025-03-10T07:02:54","date_gmt":"2025-03-10T07:02:54","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/10\/2503-04855\/"},"modified":"2025-03-10T07:02:54","modified_gmt":"2025-03-10T07:02:54","slug":"2503-04855","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/10\/2503-04855\/","title":{"rendered":"A characterization of sample adaptivity in UCB data"},"content":{"rendered":"<p>    A characterization of sample adaptivity in UCB data<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2503.04855v1 Announce Type: new<br \/>\nAbstract: We characterize a joint CLT of the number of pulls and the sample mean reward of the arms in a stochastic two-armed bandit environment under UCB algorithms. Several implications of this result are in place: (1) a nonstandard CLT of the number of pulls hence pseudo-regret that smoothly interpolates between a standard form in the large arm gap regime and a slow-concentration form in the small arm gap regime, and (2) a heuristic derivation of the sample bias up to its leading order from the correlation between the number of pulls and sample means. Our analysis framework is based on a novel perturbation analysis, which is of broader interest on its own.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Yilun Chen, Jiaqi Lu<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2503.04855\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A characterization of sample adaptivity in UCB data arXiv:2503.04855v1 Announce Type: new Abstract: We characterize a joint CLT of the number of pulls and the sample mean reward of the arms in a stochastic two-armed bandit environment under UCB algorithms. Several implications of this result are in place: (1) a nonstandard CLT of the number [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,420,112],"tags":[201,31,658],"class_list":["post-2308","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-pr","category-stat-ml","tag-number","tag-sample","tag-ucb"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2308"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=2308"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2308\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}