Supermartingales in Prediction with Expert Advice

Chernov, Alexey, Kalnishkan, Yuri, Zhdanov, Fedor and Vovk, Vladimir

(2010)

Chernov, Alexey, Kalnishkan, Yuri, Zhdanov, Fedor and Vovk, Vladimir (2010) Supermartingales in Prediction with Expert Advice.

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Abstract

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 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.

Information about this Version

This is a Submitted version
This version's date is: 10/3/2010
This item is not peer reviewed

Link to this Version

https://repository.royalholloway.ac.uk/items/1d2610bd-0673-c999-da79-8d7c1cf0ce5a/5/

Item TypeMonograph (Working Paper)
TitleSupermartingales in Prediction with Expert Advice
AuthorsChernov, Alexey
Kalnishkan, Yuri
Zhdanov, Fedor
Vovk, Vladimir
Uncontrolled Keywordscs.LG
DepartmentsFaculty of Science\Computer Science

Identifiers

Deposited by Research Information System (atira) on 03-Jul-2014 in Royal Holloway Research Online.Last modified on 03-Jul-2014

Notes

37 pages


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