  Boosting is a well-known method for improving the accuracy of weak learners
in machine learning. However, its theoretical generalization guarantee is
missing in literature. In this paper, we propose an efficient boosting method
with theoretical generalization guarantees for binary classification. Three key
ingredients of the proposed boosting method are: a) the
\textit{fully-corrective greedy} (FCG) update in the boosting procedure, b) a
differentiable \textit{squared hinge} (also called \textit{truncated
quadratic}) function as the loss function, and c) an efficient alternating
direction method of multipliers (ADMM) algorithm for the associated FCG
optimization. The used squared hinge loss not only inherits the robustness of
the well-known hinge loss for classification with outliers, but also brings
some 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 be
further improved to ${\cal O}((m/\log m)^{-1/2})$ if certain additional noise
assumption is imposed, where $m$ is the size of sample set. Both derived
learning rates are the best ones among the existing generalization results of
boosting-type methods for classification. Moreover, an efficient early stopping
scheme is provided for the proposed method. A series of toy simulations and
real data experiments are conducted to verify the developed theories and
demonstrate the effectiveness of the proposed method.
