Learning Functions of Halfspaces

Abstract: We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}<sup>n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log n)<sup>{O(k)}}$. This is the first algorithm that can PAC learn even intersections of two halfspaces in time $2<sup>{o(n)}.$