🤖 AI Summary
This work investigates the sample efficiency of classical boosting algorithms—particularly AdaBoost—in transforming weak learners into strong learners.
Method: Leveraging PAC learning theory and generalization error analysis, we construct the first rigorous counterexample to characterize the fundamental limits of AdaBoost and its canonical variants.
Contribution/Results: We establish a tight Ω(log(1/ε)) lower bound on their sample complexity, thereby proving that these algorithms are asymptotically suboptimal—refuting the long-standing conjecture that AdaBoost achieves optimal sample complexity. Specifically, AdaBoost incurs at least a logarithmic multiplicative overhead relative to the information-theoretic optimum. Our result not only provides the first precise characterization of the inherent sample complexity gap but also lays a foundational theoretical basis for designing new boosting algorithms with provably superior sample efficiency.
📝 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.
