A PTAS for Agnostically Learning Halfspaces

Abstract

We present a PTAS for agnostically learning halfspaces w.r.t. the uniform distribution on the d dimensional sphere. Namely, we show that for every >0 there is an algorithm that runs in time poly(d,1), and is guaranteed to return a classifier with error at most (1+)opt+, where opt is the error of the best halfspace classifier. This improves on Awasthi, Balcan and Long [ABL14] who showed an algorithm with an (unspecified) constant approximation ratio. Our algorithm combines the classical technique of polynomial regression (e.g. [LMN89, KKMS05]), together with the new localization technique of [ABL14].

Tasks

Reproductions