Exact learning algorithms, betting games, and circuit lower bounds

Authors:
Ryan C. Harkins;John M. Hitchcock
Affiliations:
Department of Computer Science, University of Wyoming;Department of Computer Science, University of Wyoming
Venue:
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Year:
2011

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Abstract

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