The Weighted Majority Algorithm

We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials with a prediction to be made in each and the goal of the learner is to make few mistakes We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well but the learner does not know which one A simple and e ective method based on weighted voting is introduced for constructing a compound algorithm in such a circumstance We call this method the Weighted Majority Algorithm We show that this algorithm is robust in the presence of errors in the data We discuss various versions of the Weighted Majority Algorithm and prove mistake bounds for them that are closely related to the mistake bounds of the best algorithms of the pool For example given a sequence of trials if there is an algorithm in the pool A that makes at most m mistakes then the Weighted Majority Algorithm will make at most c log jAj m mistakes on that sequence where c is xed constant