{"id":381,"date":"2024-12-05T07:03:20","date_gmt":"2024-12-05T07:03:20","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2024\/12\/05\/2412-02988\/"},"modified":"2024-12-05T07:03:20","modified_gmt":"2024-12-05T07:03:20","slug":"2412-02988","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2024\/12\/05\/2412-02988\/","title":{"rendered":"Preference-based Pure Exploration"},"content":{"rendered":"<p>    Preference-based Pure Exploration<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2412.02988v1 Announce Type: new<br \/>\nAbstract: We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $mathcal{C}$ and our the goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower bound on the sample complexity for identifying the most preferred policy with confidence level $1-delta$. Our lower bound elicits the role played by the geometry of the preference cone and punctuates the difference in hardness compared to existing best-arm identification variants of the problem. We further explicate this geometry when rewards follow Gaussian distributions. We then provide a convex relaxation of the lower bound. and leverage it to design Preference-based Track and Stop (PreTS) algorithm that identifies the most preferred policy. Finally, we show that sample complexity of PreTS is asymptotically tight by deriving a new concentration inequality for vector-valued rewards.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Apurv Shukla, Debabrota Basu<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2412.02988\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Preference-based Pure Exploration arXiv:2412.02988v1 Announce Type: new Abstract: We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $mathcal{C}$ and our the goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[189,456,457],"class_list":["post-381","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-based","tag-preference","tag-rewards"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/381"}],"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=381"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/381\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}