Prediction with Expert Evaluators’ Advice
We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner’s and his own performance using a loss function that may change over time and may be different from the loss functions used by the other experts. The learner’s goal is to perform better or not much worse than each expert, as evaluated by that expert, for all experts simultaneously. If the loss functions used by the experts are all proper scoring rules and all mixable, we show that the defensive forecasting algorithm enjoys the same performance guarantee as that attainable by the Aggregating Algorithm in the standard setting and known to be optimal. This result is also applied to the case of “specialist” experts. In this case, the defensive forecasting algorithm reduces to a simple modification of the Aggregating Algorithm.
KeywordsLoss Function Expert Advice Specialist Expert Performance Guarantee Cumulative Loss
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- 3.Freund, Y., Schapire, R.E., Singer, Y., Warmuth, M.K.: Using and combining predictors that specialize. In: Proceedings of the Twenty Ninth Annual ACM Symposium on Theory of Computing, New York, Association for Computing Machinery, pp. 334–343 (1997)Google Scholar
- 4.Chernov, A., Vovk, V.: Prediction with expert evaluators’ advice. Technical Report arXiv:0902.4127 [cs.LG], arXiv.org e-Print archive (2009)Google Scholar
- 8.Dawid, A.P.: Probability forecasting. In: Kotz, S., Johnson, N.L., Read, C.B. (eds.) Encyclopedia of Statistical Sciences, vol. 7, pp. 210–218. Wiley, New York (1986)Google Scholar
- 11.Vovk, V.: Defensive forecasting for optimal prediction with expert advice. Technical Report arXiv:0708.1503 [cs.LG], arXiv.org e-Print archive (August 2007)Google Scholar
- 15.Vovk, V., Takemura, A., Shafer, G.: Defensive forecasting. In: Cowell, R.G., Ghahramani, Z. (eds.) Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, Savannah Hotel, Barbados, Society for Artificial Intelligence and Statistics, January 6-8, pp. 365–372 (2005), http://www.gatsby.ucl.ac.uk/aistats/