EQUIVALENCE OF MODELS FOR POLYNOMIAL LEARNABILITY

In this paper we consider several variants of Valiant's learnability model that have appeared in the literature. We give conditions under which these models are equivalent in terms of the polynomially learnable concept classes they define. These equivalences allow comparisons of most of the existing theorems in Valiant-style learnability and show that several simplifying assumptions on polynomial learning algorithms can be made without loss of generality. We also give a useful reduction of learning problems to the problem of finding consistent hypotheses, and give comparisons and equivalences between Valiant's model and the prediction learning models of Haussler, Littlestone, and Warmuth (in "29th Annual IEEE Symposium on Foundations of Computer Science," 1988). © 1991.