Exact learning algorithms, betting games, and circuit lower bounds

Abstract

This paper extends and improves work of Fortnow and Klivans [5], who showed that if a circuit class has an efficient learning algorithm in Angluin's model of exact learning via equivalence and membership queries [2], then we have the lower bound EXP NP . We use entirely different techniques involving betting games [4] to remove the NP oracle and improve the lower bound to EXP . This shows that it is even more difficult to design a learning algorithm for than the results of Fortnow and Klivans indicated. © 2011 Springer-Verlag.