Chapter

Algorithmic Learning Theory

Volume 5254 of the series Lecture Notes in Computer Science pp 199-213

Supermartingales in Prediction with Expert Advice

  • Alexey ChernovAffiliated withComputer Learning Research Centre, Department of Computer Science Royal Holloway, University of London
  • , Yuri KalnishkanAffiliated withComputer Learning Research Centre, Department of Computer Science Royal Holloway, University of London
  • , Fedor ZhdanovAffiliated withComputer Learning Research Centre, Department of Computer Science Royal Holloway, University of London
  • , Vladimir VovkAffiliated withComputer Learning Research Centre, Department of Computer Science Royal Holloway, University of London

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Abstract

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.