Supermartingales in Prediction with Expert Advice

Alexey Chernov; Yuri Kalnishkan; Fedor Zhdanov; Vladimir Vovk

doi:10.1007/978-3-540-87987-9_19

Supermartingales in Prediction with Expert Advice

Alexey Chernov, Yuri Kalnishkan, Fedor Zhdanov, Vladimir Vovk

University of Brighton

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

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.

Original language	English
Title of host publication	19th International Conference, ALT 2008
Place of Publication	Berlin
Publisher	Springer
Pages	199-213
Number of pages	15
Volume	5254
DOIs	https://doi.org/10.1007/978-3-540-87987-9_19
Publication status	Published - 31 Dec 2008
Event	19th International Conference, ALT 2008 - Budapest, Hungary, October 13-16, 2008 Duration: 31 Dec 2008 → …

Conference

Conference	19th International Conference, ALT 2008
Period	31/12/08 → …

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-87987-9_19

Access to Document

10.1007/978-3-540-87987-9_19Licence: Unspecified

SG_ALT.pdfAccepted author manuscript, 207 KBLicence: Unspecified

Cite this

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title = "Supermartingales in Prediction with Expert Advice",

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{\textquoteright}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.",

author = "Alexey Chernov and Yuri Kalnishkan and Fedor Zhdanov and Vladimir Vovk",

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AU - Kalnishkan, Yuri

AU - Zhdanov, Fedor

AU - Vovk, Vladimir

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N2 - 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.

AB - 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.

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