Learning switching concepts

  • Authors:
  • Avrim Blum;Prasad Chalasani

  • Affiliations:
  • School of Computer Science, Carnegie Mellon University, Pittsburgh, PA;School of Computer Science, Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
  • Year:
  • 1992

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Abstract

We consider learning in situations where the function used to classify examples may switch back and forth between a small number of different concepts during the course of learning. We examine several models for such situations: oblivious models in which switches are made independent of the selection of examples, and more adversarial models in which a single adversary controls both the concept switches and example selections.We show relationships between the more benign models and the p-concepts of Kearns and Schapire, and present polynomial-time algorithms for learning switches between two k-DNF formulas. For the most adversarial model, we present a model of success patterned after the popular competitive analysis used in studying on-line algorithms. We describe a randomized query algorithm for such adversarial switches between two monotone disjunctions that is “1-competitive” in that the total number of mistakes plus queries is with high probability bounded by the number of switches plus some fixed polynomial in n (the number of variables).We also use notions described here to provide sufficient conditions under which learning a p-concept class “with a decision rule” implies being able to learn the class “with a model of probability.”.