Supermartingales in prediction with expert advice

Alexey Chernov, Yuri Kalnishkan, Fedor Zhdanov

Research output: Contribution to journalArticlepeer-review


We apply 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. We discuss also 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, we outline an application of defensive forecasting to a setting with several loss functions.
Original languageEnglish
Pages (from-to)2647-2669
Number of pages23
JournalTheoretical Computer Science
Issue number29-30
Publication statusPublished - 17 Jun 2010

Bibliographical note

© 2010. This manuscript version is made available under the CC-BY-NC-ND 4.0 license


  • Prediction with expert advice
  • Defensive forecasting algorithm
  • Aggregating algorithm


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