Algorithms and Lower Bounds for On-Line Learning of Geometrical Concepts

  • Authors:
  • Wolfgang Maass;Gyö/rgy Turá/n

  • Affiliations:
  • Institute for Theoretical Computer Science, Technische Universitä/t Graz, Klosterwiesgasse 32/2, A-8010 Graz, Austria. maass@igi.tu-graz.ac.at;Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60680&semi/ and Automata Theory Research Group of the Hungarian Academy of Sciences, ...

  • Venue:
  • Machine Learning
  • Year:
  • 1994

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Abstract

The complexity of on-line learning is investigated for the basic classes of geometrical objects over a discrete (“digitized”) domain. In particular, upper and lower bounds are derived for the complexity of learning algorithms for axis-parallel rectangles, rectangles in general position, balls, half-spaces, intersections of half-spaces, and semi-algebraic sets. The learning model considered is the standard model for on-line learning from counterexamples.