Supermartingales in prediction with expert advice

  • Authors:
  • Alexey Chernov;Yuri Kalnishkan;Fedor Zhdanov;Vladimir Vovk

  • Affiliations:
  • Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

Quantified Score

Hi-index 5.23

Visualization

Abstract

The paper applies the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. The paper also discusses a new setting where the experts can give advice conditional on the learner's future decision. Both the algorithms can be adapted to the new setting and give the same performance guarantees as in the traditional setting. Finally, an application of defensive forecasting to a setting with several loss functions is outlined.