Supermartingales in Prediction with Expert Advice

  • Alexey Chernov
  • Yuri Kalnishkan
  • Fedor Zhdanov
  • Vladimir Vovk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5254)


This paper compares two methods of prediction with expert advice, the Aggregating Algorithm and the Defensive Forecasting, in two different settings. The first setting is traditional, with a countable number of experts and a finite number of outcomes. Surprisingly, these two methods of fundamentally different origin lead to identical procedures. In the second setting the experts can give advice conditional on the learner’s future decision. Both methods can be used in the new setting and give the same performance guarantees as in the traditional setting. However, whereas defensive forecasting can be applied directly, the AA requires substantial modifications.


Loss Function Expert Advice Probability Forecast Traditional Setting Quadratic Loss Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alexey Chernov
    • 1
  • Yuri Kalnishkan
    • 1
  • Fedor Zhdanov
    • 1
  • Vladimir Vovk
    • 1
  1. 1.Computer Learning Research Centre, Department of Computer Science Royal HollowayUniversity of LondonEghamUK

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