Dagstuhl Seminar Proceedings. 09421 - Algebraic Methods in Computational Complexity
Doi
Abstract
We study the problem of learning parity functions that depend on at most k variables (k-parities) attribute-efficiently in the mistake-bound model.
We design a simple, deterministic, polynomial-time algorithm for learning k-parities with mistake bound O(n1−fracck), for any constant c>0. This is the first polynomial-time algorithms that learns omega(1)-parities in the mistake-bound model with mistake bound o(n).
Using the standard conversion techniques from the mistake-bound model to the PAC model, our algorithm can also be used for learning k-parities in the PAC model. In particular, this implies a slight improvement on the results of Klivans and Servedio
cite{rocco} for learning k-parities in the PAC model.
We also show that the widetildeO(nk/2) time algorithm from cite{rocco} that PAC-learns k-parities with optimal sample complexity can be extended to the mistake-bound model