On Bayes methods for on-line Boolean prediction

We examine a general Bayesian framework for constructing on-line prediction algorithms in the experts setting. These algorithms predict the bits of an unknown Boolean sequence using the advice of a finite set of experts. In this framework we use probabilistic assumptions on the unknown sequence to motivate prediction strategies. However, the relative bounds that we prove on the number of prediction mistakes made by these strategies hold for any sequence. The Bayesian framework provides a unified derivation and analysis of previously known prediction strategies, such as the Weighted Majority and Binomial Weighting algorithms. Furthermore, it provides a principled way of automatically adapting the parameters of Weighted Majority to the sequence, in contrast to previous ad hoc doubling techniques. Finally, we discuss the generalization of our methods to algorithms making randomized predictions.