Cryptographic Hardness Results for Learning Intersections of Halfspaces

We give the first representation-independent hardness results for PAC learning intersections of halfspaces, a central concept class in computational learning theory. Our hardness results are derived from two public-key cryptosystems due to Regev, which are based on the worstcase hardness of well-studied lattice problems. Specifically, we prove that a polynomial-time algorithm for PAC learning intersections of n halfspaces (for a constant > 0) in n dimensions

• Type: Journal
• Year: 2006
• Where: ECCC
• Authors: Adam R. Klivans, Alexander A. Sherstov
• Keywords: Central Concept Class, Computational Learning Theory, ECCC 2006, Well-studied Lattice Problems