Online learning versus offline learning

We present an off-line variant of the mistake-bound model of learning. This is an intermediate model between the on-line learning model (Littlestone, 1988, Littlestone, 1989) and the self-directed learning model (Goldman, Rivest & Schapire, 1993, Goldman & Sloan, 1994). Just like in the other two models, a learner in the off-line model has to learn an unknown concept from a sequence of elements of the instance space on which it makes ''guess and test'' trials. In all models, the aim of the learner is to make as few mistakes as possible. The difference between the models is that, while in the on-line model only the set of possible elements is known, in the off-line model the sequence of elements (i.e., the identity of the elements as well as the order in which they are to be presented) is known to the learner in advance. On the other band, the learner is weaker than the self-directed ]earner, which is allowed to choose adaptively the sequence of elements presented to him. We study some of the fundamental properties of the off-line model. In particular, we compare the number of mistakes made by the off-line learner on certain concept classes to those made by the on-line and self-directed learners. We give bounds on the possible gaps between the various models and show examples that prove that our bounds are tight. Another contribution of this paper is the extension of the combinatorial tool of labeled trees to a unified approach that captures the various mistake bound measures of all the models discussed. We believe that this tool will prove to be useful for further study of models of incremental learning.