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, called the Binning algorithm, and show that it is optimal in a relaxed setting in which we consider experts as continous quantities. The algorithm is efficient and near-optimal in the standard experts setting.