Sample-Near-Optimal Agnostic Boosting with Improved Running Time

2026-01-16

AI Summary

This work proposes the first agnostic boosting algorithm that simultaneously achieves near-optimal sample complexity and polynomial runtime. In the assumption-free agnostic setting, boosting has long faced a fundamental trade-off between statistical efficiency and computational tractability. Addressing this challenge, the authors introduce a novel polynomial-time algorithm grounded in agnostic learning theory. When all other parameters are fixed, the algorithm’s runtime scales polynomially with the sample size—a significant improvement over prior methods that required exponential time. This advancement marks the first unification of computational efficiency and near-optimal sample complexity in agnostic boosting, substantially enhancing its practical applicability while maintaining theoretical guarantees.

Technology Category

Machine Learning: Learning TheorySearch and Optimization: Learning to SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingResponsible Web: Algorithmic accountability and transparency on the web

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.

Problem

• agnostic boosting
• sample complexity
• running time
• weak learners
• strong learners

Innovation

• agnostic boosting
• sample complexity
• polynomial time
• weak learners
• boosting algorithm