## Convex Set Disjointness, Distributed Learning of Halfspaces, and Linear Programming

Shay Moran

Member, School of Mathematics

May 12, 2020

Distributed learning protocols are designed to train on distributed data without gathering it all on a single centralized machine, thus contributing to the efficiency of the system and enhancing its privacy. We study a central problem in distributed learning, called Distributed Learning of Halfspaces: let U \subset R^d be a known domain of size n and let h:R^d —> R be an unknown target affine function. A set of examples {(u,b)} is distributed between several parties, where u \in U is a point and b = sign(h(u)) \in {-1, +1} is its label.