Structural Results About On-line Learning Models With and Without Queries

  • Authors:
  • Peter Auer;Philip M. Long

  • Affiliations:
  • Institute for Theoretical Computer Science, Graz University of Technology, Klosterwiesgasse 32/2, A-8010 Graz, Austria. pauer@igi.tu-graz.ac.at;Department of Computer Science, National University of Singapore, Singapore 119260, Republic of Singapore. plong@comp.nus.edu.sg

  • Venue:
  • Machine Learning
  • Year:
  • 1999

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Abstract

We solve an open problem of Maass and Turán, showingthat the optimal mistake-bound when learning a given concept classwithout membership queries is within a constant factor of the optimalnumber of mistakes plus membership queries required by an algorithmthat can ask membership queries. Previously known results imply thatthe constant factor in our bound is best possible.We then show that,in a natural generalization of the mistake-bound model, the usefulnessto the learner of arbitrary “yes-no” questions between trials isvery limited. We show that several natural structural questions aboutrelatives of the mistake-bound model can be answered through theapplication of this general result. Most of these results can beinterpreted as saying that learning in apparently less powerful (andmore realistic) models is not much more difficult than learning inmore powerful models.