On the hardness of learning intersections of two halfspaces
We show that unless NP = RP, it is hard to (even) weakly PAC-learn intersection of two halfspaces in R(n) using a hypothesis which is a function of up to l halfspaces (linear threshold functions) for any integer l. Specifically, we show that for every integer l and an arbitrarily small constant epsilon > 0, unless NP = RP, no polynomial time algorithm can distinguish whether there is an intersection of two halfspaces that correctly classifies a given set of labeled points in R(n), or whether any function of l halfspaces can correctly classify at most 1/2 + epsilon fraction of the points. (C) 2010 Elsevier Inc. All rights reserved.
hardness learning halfspaces approximation