Boosting and Hard-Core Sets

This paper connects two fundamental ideas from theoretical computer science: hard-core set construction, a type of hardness amplification from computational complexity, and boosting, a technique from computational learning theory. Using this connection we give fruitful applications of complexity-theoretic techniques to learning theory and vice versa. We show that the hard-core set construction of Impagliazzo [15], which establishes the existence of distributions under which boolean functions are highly inapproximable, may be viewed as a boosting algorithm. Using alternate boosting methods we give an improved bound for hard-core set construction which matches known lower bounds from boosting and thus is optimal within this class of techniques. We then show how to apply techniques from [15] to give a new version of Jackson's celebrated Harmonic Sieve algorithm for learning DNF formulae under the uniform distribution using membership queries. Our new version has a significant asympt...

• Type: Conference
• Year: 1999
• Where: FOCS
• Authors: Adam Klivans, Rocco A. Servedio
• Keywords: Boosting, FOCS 1999, Hard-core Set Constructions, Learning Theory, Theoretical Computer Science