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 (Lit tlestone, 1988, Littlestone, 1989) and the self-directed learning mode l (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 be tween the models is that, while in the on-line model only the set of p ossible elements is known, in the off-line model the sequence of eleme nts (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 o ther 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 mode l. In particular, we compare the number of mistakes made by the off-li ne learner on certain concept classes to those made by the on-line and self-directed learners. We give bounds on the possible gaps between t he various models and show examples that prove that our bounds are tig ht. Another contribution of this paper is the extension of the combina torial tool of labeled trees to a unified approach that captures the v arious 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.