New revision algorithms

Abstract

A revision algorithm is a learning algorithm that identifies the target concept, starting from an initial concept. Such an algorithm is considered efficient if its complexity (in terms of the resource one is interested in) is polynomial in the syntactic distance between the initial and the target concept, but only polylogarithmic in the number of variables in the universe. We give efficient revision algorithms in the model of learning with equivalence and membership queries. The algorithms work in a general revision model where both deletion and addition type revision operators are allowed. In this model one of the main open problems is the efficient revision of Horn sentences. Two revision algorithms are presented for special cases of this problem: for depth-1 acyclic Horn sentences, and for definite Horn sentences with unique heads. We also present an efficient revision algorithm for threshold functions. © Springer-Verlag Berlin Heidelberg 2004.