<?xml version="1.0"?>
<oembed><version>1.0</version><provider_name>Microsoft Research</provider_name><provider_url>https://www.microsoft.com/en-us/research</provider_url><author_name>Brenda Potts</author_name><author_url>https://www.microsoft.com/en-us/research/people/v-brpotts/</author_url><title>Understanding the Eluder Dimension - Microsoft Research</title><type>rich</type><width>600</width><height>338</height><html>&lt;blockquote class="wp-embedded-content" data-secret="KCGml2fC6A"&gt;&lt;a href="https://www.microsoft.com/en-us/research/publication/understanding-the-eluder-dimension/"&gt;Understanding the Eluder Dimension&lt;/a&gt;&lt;/blockquote&gt;&lt;iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/publication/understanding-the-eluder-dimension/embed/#?secret=KCGml2fC6A" width="600" height="338" title="&#x201C;Understanding the Eluder Dimension&#x201D; &#x2014; Microsoft Research" data-secret="KCGml2fC6A" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"&gt;&lt;/iframe&gt;&lt;script type="text/javascript"&gt;
/* &lt;![CDATA[ */
/*! This file is auto-generated */
!function(d,l){"use strict";l.querySelector&amp;&amp;d.addEventListener&amp;&amp;"undefined"!=typeof URL&amp;&amp;(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&amp;&amp;!/[^a-zA-Z0-9]/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret="'+t.secret+'"]'),o=l.querySelectorAll('blockquote[data-secret="'+t.secret+'"]'),c=new RegExp("^https?:$","i"),i=0;i&lt;o.length;i++)o[i].style.display="none";for(i=0;i&lt;a.length;i++)s=a[i],e.source===s.contentWindow&amp;&amp;(s.removeAttribute("style"),"height"===t.message?(1e3&lt;(r=parseInt(t.value,10))?r=1e3:~~r&lt;200&amp;&amp;(r=200),s.height=r):"link"===t.message&amp;&amp;(r=new URL(s.getAttribute("src")),n=new URL(t.value),c.test(n.protocol))&amp;&amp;n.host===r.host&amp;&amp;l.activeElement===s&amp;&amp;(d.top.location.href=t.value))}},d.addEventListener("message",d.wp.receiveEmbedMessage,!1),l.addEventListener("DOMContentLoaded",function(){for(var e,t,s=l.querySelectorAll("iframe.wp-embedded-content"),r=0;r&lt;s.length;r++)(t=(e=s[r]).getAttribute("data-secret"))||(t=Math.random().toString(36).substring(2,12),e.src+="#?secret="+t,e.setAttribute("data-secret",t)),e.contentWindow.postMessage({message:"ready",secret:t},"*")},!1)))}(window,document);
//# sourceURL=https://www.microsoft.com/en-us/research/wp-includes/js/wp-embed.min.js
/* ]]&gt; */
&lt;/script&gt;
</html><description>We provide new insights on eluder dimension, a complexity measure that has been extensively used to bound the regret of algorithms for online bandits and reinforcement learning with function approximation. First, we study the relationship between the eluder dimension for a function class and a generalized notion of rank, defined for any monotone &#x201C;activation&#x201D;&#xA0;&#x3C3;:R&#x2192;R, which [&hellip;]</description></oembed>
