Supermartingales in Prediction with Expert Advice
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.
KeywordsLoss Function Expert Advice Probability Forecast Traditional Setting Quadratic Loss Function
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- 11.Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1996)Google Scholar
- 15.Vovk, V.: Aggregating Strategies. In: Fulk, M., Case, J. (eds.) Proceedings of the Third Annual Workshop on Computational Learning Theory, San Mateo, CA, pp. 371–383 (1990)Google Scholar
- 17.Vovk, V.: Competitive on-line learning with a convex loss function. Technical Report arXiv:cs/0506041v3 [cs.LG], arXiv.org e-Print archive (September 2005)Google Scholar
- 18.Vovk, V.: On-line regression competitive with reproducing kernel Hilbert spaces. Technical Report arXiv:cs/0511058v2 [cs.LG], arXiv.org e-Print archive (January 2006)Google Scholar
- 19.Vovk, V.: Metric entropy in competitive on-line prediction. Technical Report arXiv:cs/0609045v1 [cs.LG], arXiv.org e-Print archive (September 2006)Google Scholar
- 20.Vovk, V.: Continuous and randomized defensive forecasting: unified view. Technical Report arXiv:0708.2353v2 [cs.LG], arXiv.org e-Print archive (August 2007)Google Scholar