<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); word-wrap: break-word; line-break: after-white-space;"><div dir="auto" class="" style="word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><b class=""><font color="#000000" class=""><span class="" style="font-size: 14px;">University of Chicago </span></font></b></font></div><div dir="auto" class="" style="word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><font color="#000000" class=""><span class="" style="font-size: 14px;"><b class="">Toyota Technological Institute at Chicago Machine Learning Seminar Series</b></span></font></font></div><div class=""><font face="Arial" class=""><font color="#000000" class=""><span class="" style="font-size: 14px;"><b class=""><br class=""></b></span></font></font></div></div><div dir="auto" class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><br class=""><b class="" style="font-size: 14px;">Shay Moran</b><br class=""><span class="" style="font-size: 14px;">Technion</span><br class=""><br class=""><b class="" style="font-size: 14px;">Friday, October 25, 2019 at 10:30 - 11:30 am<br class=""></b><b class=""><span class="" style="font-size: 11pt; font-family: Arial, sans-serif;">TTIC, </span></b> <b class=""><span class="" style="font-size: 11pt; font-family: Arial, sans-serif;">Room 526</span></b> <br class=""><br class=""><br class=""><b class="" style="font-size: 14px;">Title:</b></font></div><div dir="auto" class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><font color="#000000" class=""><span class="" style="font-size: 15.333333015441895px;">Convex Set Disjointness, Distributed Learning of Halfspaces and LP Feasibility</span></font><br class=""><b class="" style="font-size: 14px;"><font face="Arial" class="" style="font-weight: normal;"><b class=""><br class=""></b></font></b></font></div><div dir="auto" class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><span class=""><font face="Arial" class="" style="font-size: 14px;"><b class="">Abstract:</b><br class=""></font><div class=""><font color="#000000" class=""><span class="" style="font-size: 14px;">We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain U\subset R^d of size | U | = n. Their mutual goal is to decide using minimum communication whether the convex hulls of their sets intersect (equivalently, whether their sets can be separated by a hyperplane).<br class=""><br class=""></span></font></div><div class=""><font color="#000000" class=""><span class="" style="font-size: 14px;">Different forms of this problem naturally arise in distributed learning and optimization: it is equivalent to Distributed Linear Program (LP) Feasibility — a basic task in distributed optimization, and it is tightly linked to Distributed Learning of Halfdpaces in R^d.<br class="">In communication complexity theory, CSD can be viewed as a geometric interpolation between the classical problems of Set Disjointness (when d>= n-1) and Greater-Than (when d=1).<br class=""><br class=""></span></font></div><div class=""><font color="#000000" class=""><span class="" style="font-size: 14px;">We establish a nearly tight bound of ~Theta(d log n) on the communication complexity of learning halfspaces in R^d.<br class="">For Convex Set Disjointness (and the equivalent task of distributed LP feasibility) we derive upper and lower bounds of tilde O(d^2\log n) and ~Omega(d\log n). These results improve upon several previous works in distributed learning and optimization.<br class="">Unlike typical works in communication complexity, the main technicalThese geometric statements are used by our protocols to provide a compressed summary of the players’ input. Joint work with Mark Braverman, Gillat Kol, and Raghuvansh R. Saxena (Princeton University).<br class=""> </span></font></div><font face="Arial" class="" style="font-size: 14px;"><br class=""><b class="">Bio:</b><br class=""></font><font color="#000000" class=""><span class="" style="font-size: 14px;">Shay Moran is a visiting researcher at Google Brain, Princeton. He graduated from the Technion in late 2016 and since then he spent one year in California (UCSD and Simons Institute) and two years in Princeton (IAS and Princeton University). In October ’20 he will join the mathematics department at the Technion as an assistant Professor. His research interests revolve around mathematical problems in computer science, with a special focus on combinatorial-geometric problems inspired by machine learning.<br class=""><b class=""><br class=""></b></span></font></span></font></div><div dir="auto" class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); word-wrap: break-word; line-break: after-white-space;"><font face="Arial" class=""><span class=""><font color="#000000" class=""><span class="" style="font-size: 14px;"><b class="">Host: Rebecca Willett </b> </span></font></span></font></div><div class=""></div></body></html>