Cryptographic Hardness 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 polynomialtime algorithm for PAC learning intersections of nε halfspaces (for a constant ε > 0) in n

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Adam R. Klivans, Alexander A. Sherstov
• Keywords: Computational Learning Theory, FOCS 2006, PAC Learning Intersections, Theoretical Computer Science, first Representation-independent Hardness