{"id":190142,"date":"2013-11-20T00:00:00","date_gmt":"2013-11-22T17:10:41","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/two-basic-problems-in-finite-stochastic-optimization\/"},"modified":"2016-08-02T06:11:52","modified_gmt":"2016-08-02T13:11:52","slug":"two-basic-problems-in-finite-stochastic-optimization","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/two-basic-problems-in-finite-stochastic-optimization\/","title":{"rendered":"Two basic problems in finite stochastic optimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>I will present a new theoretical perspective on two basic problems arising in stochastic optimization. The first one is arguably the most elementary problem in stochastic optimization: assume that one wants to find the maximum of function defined on a finite set, and that one is given a budget of n noisy evaluations. What is the best sequential allocation procedure for the evaluations? The second problem that I will discuss is inspired from the issue of security analysis of a power system. We formalize this problem as follows: Let X be a set, and A a subset of X of &#8220;interesting&#8221; elements in X. One can access X only through requests to a finite set of probabilistic experts. More precisely, when one makes a request to the i<sup>th<\/sup> expert, the latter draws independently at random a point from a fixed probability distribution P<sub>i<\/sub> over X. One is interested in discovering rapidly as many elements of A as possible, by making sequential requests to the experts.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I will present a new theoretical perspective on two basic problems arising in stochastic optimization. The first one is arguably the most elementary problem in stochastic optimization: assume that one wants to find the maximum of function defined on a finite set, and that one is given a budget of n noisy evaluations. What is [&hellip;]<\/p>\n","protected":false},"featured_media":197991,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-190142","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/MSGnrHojwSk\/","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190142","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190142\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197991"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=190142"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=190142"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=190142"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=190142"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=190142"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=190142"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=190142"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=190142"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=190142"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=190142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}