{"id":8303,"date":"2025-11-12T07:03:16","date_gmt":"2025-11-12T07:03:16","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/11\/12\/2511-07504\/"},"modified":"2025-11-12T07:03:16","modified_gmt":"2025-11-12T07:03:16","slug":"2511-07504","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/11\/12\/2511-07504\/","title":{"rendered":"Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids"},"content":{"rendered":"<p>    Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2511.07504v1 Announce Type: new<br \/>\nAbstract: We consider the maximization of $x^top theta$ over $(x,theta) in mathcal{X} times Theta$, with $mathcal{X} subset mathbb{R}^d$ convex and $Theta subset mathbb{R}^d$ an ellipsoid. This problem is fundamental in linear bandits, as the learner must solve it at every time step using optimistic algorithms. We first show that for some sets $mathcal{X}$ e.g. $ell_p$ balls with $p&gt;2$, no efficient algorithms exist unless $mathcal{P} = mathcal{NP}$. We then provide two novel algorithms solving this problem efficiently when $mathcal{X}$ is a centered ellipsoid. Our findings provide the first known method to implement optimistic algorithms for linear bandits in high dimensions.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Raymond Zhang, H&#8217;edi Hadiji, Richard Combes<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2511.07504\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids arXiv:2511.07504v1 Announce Type: new Abstract: We consider the maximization of $x^top theta$ over $(x,theta) in mathcal{X} times Theta$, with $mathcal{X} subset mathbb{R}^d$ convex and $Theta subset mathbb{R}^d$ an ellipsoid. This problem is fundamental in linear bandits, as the learner must solve it at every time step [&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":[821,2110,1948],"class_list":["post-8303","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-algorithms","tag-mathcal","tag-theta"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8303"}],"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=8303"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8303\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=8303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=8303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=8303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}