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, UK TW20 0EX;Computer Learning Research Centre, Department of Computer Science Royal Holloway, University of London, Egham, UK TW20 0EX;Computer Learning Research Centre, Department of Computer Science Royal Holloway, University of London, Egham, UK TW20 0EX;Computer Learning Research Centre, Department of Computer Science Royal Holloway, University of London, Egham, UK TW20 0EX
Venue:
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Year:
2008

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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.