Types of Efficient Query Learning

Abstract

In this paper the problem of using queries in order to learn an unknown concept is investigated. Unfortunately, for many concept classes an exhaustive or nearly exhaustive search is necessary when using membership queries only (so named by Angluin). Not only membership queries but also superset queries and equivalence queries as defined by Angluin are considered. Furthermore, learning protocols for which efficient query learning is possible are introduced. At first, the paper introduces a characterization of concept classes where exhaustive membership queries can be avoided by using clever query strategies. The Vapnik-Chervonenkis dimension for stating an upper-bound for required membership queries is used along with a sketch of an appropriate algorithm. In addition, concept classes are characterized where one or some more positive examples provided to the learning system allow to dramatically reduce the number of required queries. Furthermore, for these concept classes the existence of efficient query strategies which use combinations of different query types is proved. A probabilistic query learning algorithm is presented as well. Finally, concept classes are characterized for which a polynomial time learning algorithm exists which uses membership queries efficiently.