{"id":569271,"date":"2019-01-24T12:30:40","date_gmt":"2019-01-24T20:30:40","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=569271"},"modified":"2019-02-22T10:44:00","modified_gmt":"2019-02-22T18:44:00","slug":"chasing-convex-bodies-from-1817-to-2018","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/chasing-convex-bodies-from-1817-to-2018\/","title":{"rendered":"Chasing convex bodies, from 1817 to 2018"},"content":{"rendered":"<p>A selector maps a set (in some set system) to an element in that set. In a metric space, Lipschitz selection is the problem of finding a selector that is Lipschitz with respect to the Hausdorff distance. A classical result is the existence of a Lipschitz selector for convex sets in Euclidean space. In this talk we will prove an *online* version of this classical result. This resolves the 1991 Friedman-Linial conjecture on convex body chasing.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A selector maps a set (in some set system) to an element in that set. In a metric space, Lipschitz selection is the problem of finding a selector that is Lipschitz with respect to the Hausdorff distance. A classical result is the existence of a Lipschitz selector for convex sets in Euclidean space. In this [&hellip;]<\/p>\n","protected":false},"featured_media":569274,"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":[13556],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-569271","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/jCVIuvkY_3M","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/569271","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":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/569271\/revisions"}],"predecessor-version":[{"id":569277,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/569271\/revisions\/569277"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/569274"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=569271"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=569271"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=569271"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=569271"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=569271"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=569271"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=569271"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=569271"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=569271"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=569271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}