Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Using and combining predictors that specialize
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A game of prediction with expert advice
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Derandomizing Stochastic Prediction Strategies
Machine Learning - Special issue: computational learning theory, COLT '97
Prediction, Learning, and Games
Prediction, Learning, and Games
Sequential prediction of individual sequences under general loss functions
IEEE Transactions on Information Theory
Supermartingales in prediction with expert advice
Theoretical Computer Science
A closer look at adaptive regret
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
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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.