Online Learning versus Offline Learning

  • Authors:
  • Shai Ben-David;Eyal Kushilevitz;Yishay Mansour

  • Affiliations:
  • Computer Science Dept., Technion, Israel. E-mail: shai@cs.technion.ac.il;Computer Science Dept., Technion, Israel. E-mail: eyalk@cs.technion.ac.il;Computer Science Dept., Tel-Aviv University, Israel. E-mail: mansour@gemini.math.tau.ac.il

  • Venue:
  • Machine Learning
  • Year:
  • 1997

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Abstract

We present an off-line variant of the mistake-bound model oflearning. This is an intermediate model between the on-line learning model (Littlestone, 1988, Littlestone, 1989) and theself-directed learning model (Goldman, Rivest& Schapire, 1993, Goldman & Sloan, 1994). Just like in theother two models, a learner in the off-line model has to learn anunknown concept from a sequence of elements of the instance space onwhich it makes “guess and test” trials. In all models,the aim of the learner is to make as few mistakes as possible. Thedifference between the models is that, while in the on-line modelonly the set of possible elements is known, in theoff-line model the sequence of elements (i.e., theidentity of the elements as well as the order in which they are to bepresented) is known to the learner in advance. On the other hand, thelearner is weaker than the self-directed learner, which is allowed tochoose 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 ofmistakes made by the off-line learner on certain concept classes tothose made by the on-line and self-directed learners. We give boundson the possible gaps between the various models and show examplesthat prove that our bounds are tight.Another contribution of this paper is the extension of thecombinatorial tool of labeled trees to a unified approach thatcaptures the various mistake bound measures of all the modelsdiscussed. We believe that this tool will prove to be useful forfurther study of models of incremental learning.