# AdaBoost is not an Optimal Weak to Strong Learner

arXiv: https://arxiv.org/abs/2301.11571 · HTML: https://mlsanity.com/paper/2301.11571/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 16 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [The Optimal Sample Complexity of PAC Learning](https://mlsanity.com/paper/1507.00473/) (2015)
- [Bagging is an Optimal PAC Learner](https://mlsanity.com/paper/2212.02264/) (2022)
- [Optimal Weak to Strong Learning](https://mlsanity.com/paper/2206.01563/) (2022)
- [Margin-Based Generalization Lower Bounds for Boosted Classifiers](https://mlsanity.com/paper/1909.12518/) (2019)

## Built on by (most cited first, 6 of 6)

- [Improved Margin Generalization Bounds for Voting Classifiers](https://mlsanity.com/paper/2502.16462/) (2025)
- [Boosting, Voting Classifiers and Randomized Sample Compression Schemes](https://mlsanity.com/paper/2402.02976/) (2024)
- [The Many Faces of Optimal Weak-to-Strong Learning](https://mlsanity.com/paper/2408.17148/) (2024)
- [Sample-Efficient Agnostic Boosting](https://mlsanity.com/paper/2410.23632/) (2024)
- [Tight Margin-Based Generalization Bounds for Voting Classifiers over Finite Hypothesis Sets](https://mlsanity.com/paper/2511.20407/) (2025)
- [Tight Generalization Bound for AdaBoost](https://mlsanity.com/paper/2607.26838/) (2026)

## Abstract (arXiv)

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.