AdaBoost is not an Optimal Weak to Strong Learner

TL;DR

This paper demonstrates that AdaBoost, a widely used boosting algorithm, is not sample-optimal and requires more data than theoretically necessary to achieve a given accuracy, unlike the recently developed optimal algorithms.

Contribution

The paper proves that AdaBoost and similar classic boosting algorithms are sub-optimal in sample complexity compared to the best possible algorithms.

Findings

AdaBoost's sample complexity is at least logarithmically higher than optimal.

Other classic boosting algorithms also exhibit sub-optimal sample complexity.

Optimal algorithms can achieve desired accuracy with fewer training samples.

Abstract

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.