Continuous Experts and the Binning Algorithm

We consider the design of online master algorithms for combining the predictions from a set of experts where the absolute loss of the master is to be close to the absolute loss of the best expert. For the case when the master must produce binary predictions, the Binomial Weighting algorithm is known to be optimal when the number of experts is large. It has remained an open problem how to design master algorithms based on binomial weights when the predictions of the master are allowed to be real valued. In this paper we provide such an algorithm and call it the Binning algorithm because it maintains experts in an array of bins. We show that this algorithm is optimal in a relaxed setting in which we consider experts as continuous quantities. The algorithm is efficient and near-optimal in the standard experts setting.

[1]  David Haussler,et al.  Sequential Prediction of Individual Sequences Under General Loss Functions , 1998, IEEE Trans. Inf. Theory.

[2]  Manfred K. Warmuth,et al.  Exponentiated Gradient Versus Gradient Descent for Linear Predictors , 1997, Inf. Comput..

[3]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[4]  Vladimir Vovk,et al.  Aggregating strategies , 1990, COLT '90.

[5]  Mark Herbster,et al.  Tracking the Best Expert , 1995, Machine-mediated learning.

[6]  Manfred K. Warmuth,et al.  The weighted majority algorithm , 1989, 30th Annual Symposium on Foundations of Computer Science.

[7]  Yoav Freund,et al.  Drifting Games and Brownian Motion , 2002, J. Comput. Syst. Sci..

[8]  David Haussler,et al.  How to use expert advice , 1993, STOC.

[9]  Manfred K. Warmuth,et al.  Additive versus exponentiated gradient updates for linear prediction , 1995, STOC '95.

[10]  Nicolò Cesa-Bianchi,et al.  Gambling in a rigged casino: The adversarial multi-armed bandit problem , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[11]  Yoav Freund,et al.  Boosting a weak learning algorithm by majority , 1990, COLT '90.

[12]  Manfred K. Warmuth,et al.  Averaging Expert Predictions , 1999, EuroCOLT.