Sample-Near-Optimal Agnostic Boosting with Improved Running Time

Abstract: Boosting is a powerful method that turns weak learners, which perform only slightly better than random guessing, into strong learners with high accuracy. While boosting is well understood in the classic setting, it is less so in the agnostic case, where no assumptions are made about the data. Indeed, only recently was the sample complexity of agnostic boosting nearly settled arXiv:2503.09384, but the known algorithm achieving this bound has exponential running time. In this work, we propose the first agnostic boosting algorithm with near-optimal sample complexity, running in time polynomial in the sample size when considering the other parameters of the problem fixed.