Tight Generalization Bound for AdaBoost

Abstract

In this paper we show that the generalization error of AdaBoost is $Θ\big(\tfrac{d\ln(nγ^{2}/d)}{nγ^2}+\tfrac{\ln(1/δ)}{n}\big)$, where ${\hat{I}}^3$ is the advantage guaranteed by the weak learner, $d$ is the VC-dimension of the class containing the weak hypotheses, $n$ is the sample size, and $\hat{I}´$ is the confidence parameter. The contribution of this paper is the upper bound; the matching lower bound follows from prior work. The upper bound proof follows by combining the known fact that AdaBoost outputs a voting classifier whose voting function has zero empirical ${\hat{I}}^3/2$-margin loss with what is, to the best of our knowledge, a new margin-based generalization bound for voting classifiers.

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