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Boosting is a well-known method for improving the accuracy of weak learnersin machine learning. However, its theoretical generalization guarantee ismissing in literature. In this paper, we propose an efficient boosting methodwith theoretical generalization guarantees for binary classification. Three keyingredients of the proposed boosting method are: a) the\textit{fully-corrective greedy} (FCG) update in the boosting procedure, b) adifferentiable \textit{squared hinge} (also called \textit{truncatedquadratic}) function as the loss function, and c) an efficient alternatingdirection method of multipliers (ADMM) algorithm for the associated FCGoptimization. The used squared hinge loss not only inherits the robustness ofthe well-known hinge loss for classification with outliers, but also bringssome benefits for computational implementation and theoretical justification.Under some sparseness assumption, we derive a fast learning rate of the order${\cal O}((m/\log m)^{-1/4})$ for the proposed boosting method, which can befurther improved to ${\cal O}((m/\log m)^{-1/2})$ if certain additional noiseassumption is imposed, where $m$ is the size of sample set. Both derivedlearning rates are the best ones among the existing generalization results ofboosting-type methods for classification. Moreover, an efficient early stoppingscheme is provided for the proposed method. A series of toy simulations andreal data experiments are conducted to verify the developed theories anddemonstrate the effectiveness of the proposed method.

Fully-Corrective Gradient Boosting with Squared Hinge: Fast Learning Rates and Early Stopping