{"id":472977,"date":"2018-02-05T00:00:34","date_gmt":"2018-02-05T08:00:34","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=472977"},"modified":"2018-03-13T09:17:09","modified_gmt":"2018-03-13T16:17:09","slug":"a-unifying-theory-of-first-order-methods-and-applications","status":"publish","type":"msr-video","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/video\/a-unifying-theory-of-first-order-methods-and-applications\/","title":{"rendered":"A Unifying Theory of First-Order Methods and Applications"},"content":{"rendered":"<div class=\"panel ng-binding\">First-order methods in optimization have become the workhorse tool in modern data-driven applications. Although various general methods with optimal iteration complexities have been known for decades, their standard analysis often appears unintuitive. In this talk, I will present a simple unifying framework based on the numerical discretization of a continuous-time dynamics. Further, I will present a novel accelerated method that is naturally obtained from this framework. The method matches the iteration complexity of the well-known Nesterov\u2019s method, and is, in some cases, more stable under noise-corrupted gradients. Time permitting, I will talk about other applications of the framework, such as in obtaining width-independent parallel algorithms for problems with positive linear constraints, and the extensions of the framework to various settings, including that of block coordinate descent.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>First-order methods in optimization have become the workhorse tool in modern data-driven applications. Although various general methods with optimal iteration complexities have been known for decades, their standard analysis often appears unintuitive. In this talk, I will present a simple unifying framework based on the numerical discretization of a continuous-time dynamics. Further, I will present [&hellip;]<\/p>\n","protected":false},"featured_media":472983,"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":[13561],"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-472977","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/SOTmUdhwNw8","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/472977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/472977\/revisions"}],"predecessor-version":[{"id":472980,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/472977\/revisions\/472980"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media\/472983"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=472977"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=472977"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=472977"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=472977"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=472977"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=472977"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=472977"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=472977"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=472977"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=472977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}