The Structure of Intrinsic Complexity of Learning

Recently, a new approach to the study of “intrinsic” complexity of learning has originated in the work of Freivalds, and has been investigated for identification in the limit of functions by Freivalds, Kinber, and Smith and for identification in the limit of languages by Jain and Sharma. Instead of concentrating on the complexity of the learning algorithm, this approach uses the notion of reducibility to investigate the complexity of the concept classes being learned. Three representative classes have been presented that classify learning problems of increasing difficulty. (a) Classes that can be learned by machines that confirm their success (singleton languages). (b) Classes that can be learned by machines that cannot confirm their success but can provide an upper bound on the number of mind changes after inspecting an element of the language (pattern languages). (c) Classes that can be learned by machines that can neither confirm success nor can provide an upper bound on the number of mind changes (finite languages).