On-line prediction and conversion strategies

Abstract

We study the problem of deterministically predicting boolean valuesby combining the boolean predictions of several experts.Previous on-line algorithms for this problem predict with the weightedmajority of the experts' predictions.These algorithms give each expert an exponential weight βmwhere β is a constant in [0,1) and m is the number of mistakesmade by the expert in the past. We show that it is better to usesums of binomials as weights.In particular, we present a deterministic algorithmusing binomial weights that has a better worst case mistake bound than thebest deterministic algorithm using exponential weights.The binomial weights naturally arise from a version space argument.We also show how both exponential and binomial weighting schemes can beused to make prediction algorithms robust against noise.