Continuous Drifting Games

Abstract

We combine the results of [5] and [3] and derive a continuous variant of a large class of drifting games. Our analysis furthers the understanding of the relationship between boosting, drifting games and Brownian motion and yields a differential equation that describes the core of the problem. 1 Introduction In [2], Freund shows that boosting is closely related to a two party game called the "majority vote game". In the last year this work was extended in two ways. First, in [5] Schapire generalizes the majority vote game to a much more general set of games, called "drifting games". He gives a recursive formula for solving these games and derives several generalizations of the boost-by-majority algorithm. Solving the game in this case requires numerical calculation of the recursive formula. Second, in [3], Freund derives an adaptive version of the boost-by-majority algorithm. To do that he considers the limit of the majority vote game when the number of boosting rounds is increased to ...