Comparison of Query Learning and Gold-Style Learning in Dependence of the Hypothesis Space

Abstract

Different formal learning models address different aspects of learning. Below we compare learning via queries —interpreting learning as a one-shot process in which the learner is required to identify the target concept with just one hypothesis—to Gold-style learning —interpreting learning as a limiting process in which the learner may change its mind arbitrarily often before converging to a correct hypothesis. Although these two approaches seem rather unrelated, a previous study has provided characterisations of different models of Gold-style learning (learning in the limit, conservative inference, and behaviourally correct learning) in terms of query learning. Thus under certain circumstances it is possible to replace limit learners by equally powerful one-shot learners. Both this previous and the current analysis are valid in the general context of learning indexable classes of recursive languages. The main purpose of this paper is to solve a challenging open problem from the previous study. The solution of this problem leads to an important observation, namely that there is a natural query learning type hierarchically in-between Gold-style learning in the limit and behaviourally correct learning. Astonishingly, this query learning type can then again be characterised in terms of Gold-style inference. In connection with this new in-between inference type we have gained new insights into the basic model of conservative learning and the way conservative learners work. In addition to these results, we compare several further natural inference types in both models to one another.