Revisiting Agnostic Boosting

Boosting is a key method in statistical learning, allowing for converting weak learners into strong ones. While well studied in the realizable case, the statistical properties of weak-to-strong learning remains less understood in the agnostic setting, where there are no assumptions on the distribution of the labels. In this work, we propose a new agnostic boosting algorithm with substantially improved sample complexity compared to prior works under very general assumptions. Our approach is based on a reduction to the realizable case, followed by a margin-based filtering step to select high-quality hypotheses. We conjecture that the error rate achieved by our proposed method is optimal up to logarithmic factors.