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Boosting algorithms produce a classifier by iteratively combining basehypotheses. It has been observed experimentally that the generalization errorkeeps improving even after achieving zero training error. One popularexplanation attributes this to improvements in margins. A common goal in a longline of research, is to maximize the smallest margin using as few basehypotheses as possible, culminating with the AdaBoostV algorithm by (R{\"a}tschand Warmuth [JMLR'04]). The AdaBoostV algorithm was later conjectured to yieldan optimal trade-off between number of hypotheses trained and the minimalmargin over all training points (Nie et al. [JMLR'13]). Our main contributionis a new algorithm refuting this conjecture. Furthermore, we prove a lowerbound which implies that our new algorithm is optimal.

Optimal Minimal Margin Maximization with Boosting