On-line Learning and the Metrical Task System Problem

  • Authors:
  • Avrim Blum;Carl Burch

  • Affiliations:
  • Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213, USA. avrim+@cs.cmu.edu;Department of Computer Science, Carnegie Mellon University, Pittsburgh PA 15213, USA. cburch+@cs.cmu.edu

  • Venue:
  • Machine Learning
  • Year:
  • 2000

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Abstract

The problem ofcombining expert advice, studied extensively in theComputational Learning Theory literature, and the Metrical TaskSystem (MTS) problem,studied extensively in the area of On-line Algorithms,contain a number of interesting similarities. In this paper weexplore the relationship between these problems andshow how algorithms designed for each can be used to achievegood bounds and new approaches for solving the other.Specific contributions of this paper include:• An analysis of how two recent algorithms for the MTSproblem can beapplied to the problem of tracking the best expert in the“decision-theoretic” setting, providing goodbounds and an approach of a much different flavor fromthe well-known multiplicative-update algorithms.• An analysis showing how the standard randomized WeightedMajority (or Hedge) algorithm can be used for the problem of“combining on-line algorithms on-line”, giving much strongerguarantees than the results of Azar, Y., Broder, A., & Manasse, M. (1993).Proc ACM-SIAM Symposium on Discrete Algorithms (pp. 432–440)when the algorithms being combinedoccupy a state space of bounded diameter.• A generalization of the above, showing how (a simplified versionof) Herbster and Warmuth's weight-sharing algorithm can be applied togive a “finely competitive” bound for the uniform-spaceMetrical Task System problem.We also give a new, simpler algorithm for tracking experts, whichunfortunately does not carry over to the MTS problem.Finally, we present an experimental comparison of how these algorithmsperform on a process migration problem, a problem that combinesaspects of both the experts-tracking and MTS formalisms.