COLT '90 Proceedings of the third annual workshop on Computational learning theory
The weighted majority algorithm
Information and Computation
Using and combining predictors that specialize
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
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
Machine Learning - Special issue on context sensitivity and concept drift
Tracking a small set of experts by mixing past posteriors
The Journal of Machine Learning Research
Prediction, Learning, and Games
Prediction, Learning, and Games
Efficient learning algorithms for changing environments
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Prediction with expert evaluators' advice
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Low-complexity sequential lossless coding for piecewise-stationary memoryless sources
IEEE Transactions on Information Theory
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For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t1,t2] is the loss of the algorithm there minus the loss of the best expert. Adaptive regret measures how well the algorithm approximates the best expert locally, and it is therefore somewhere between the classical regret (measured on all outcomes) and the tracking regret, where the algorithm is compared to a good sequence of experts. We investigate two existing intuitive methods to derive algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. Our main result is a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds can be derived. We also prove that Fixed Share is optimal, in the sense that no algorithm can have a better adaptive regret bound.