Multitask learning with expert advice

  • Authors:
  • Jacob Abernethy;Peter Bartlett;Alexander Rakhlin

  • Affiliations:
  • Department of Computer Science, UC Berkeley;Department of Computer Science, UC Berkeley and Department of Statistics, UC Berkeley;Department of Computer Science, UC Berkeley

  • Venue:
  • COLT'07 Proceedings of the 20th annual conference on Learning theory
  • Year:
  • 2007

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Abstract

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the "ideal" algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.