The weighted majority algorithm
Information and Computation
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
Efficient algorithms for online decision problems
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Prediction, Learning, and Games
Prediction, Learning, and Games
Hannan consistency in on-line learning in case of unbounded losses under partial monitoring
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Defensive universal learning with experts
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Online Learning in Case of Unbounded Losses Using Follow the Perturbed Leader Algorithm
The Journal of Machine Learning Research
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In this paper the method of prediction with expert advice is applied for learning volatility of discrete time series. We construct arbitrage strategies (or experts) which suffer gain when "micro" and "macro" volatilities of a time series differ. For merging different expert strategies in a strategy of the learner, we use some modification of Kalai and Vempala algorithm of following the perturbed leader where weights depend on current gains of the experts. We consider the case when experts onestep gains can be unbounded. New notion of a volume of a game vt is introduced. We show that our algorithm has optimal performance in the case when the one-step increments Δvt = vt -vt-1 of the volume satisfy Δvt = o(vt) as t → ∞.