  AdaBoost is a classic boosting algorithm for combining multiple inaccurate
classifiers produced by a weak learner, to produce a strong learner with
arbitrarily high accuracy when given enough training data. Determining the
optimal number of samples necessary to obtain a given accuracy of the strong
learner, is a basic learning theoretic question. Larsen and Ritzert
(NeurIPS'22) recently presented the first provably optimal weak-to-strong
learner. However, their algorithm is somewhat complicated and it remains an
intriguing question whether the prototypical boosting algorithm AdaBoost also
makes optimal use of training samples. In this work, we answer this question in
the negative. Concretely, we show that the sample complexity of AdaBoost, and
other classic variations thereof, are sub-optimal by at least one logarithmic
factor in the desired accuracy of the strong learner.
