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arXiv · 1307.1192

AdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods

Robert M. Freund·Paul Grigas·Rahul Mazumder
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Abstract

Boosting methods are highly popular and effective supervised learning methods which combine weak learners into a single accurate model with good statistical performance. In this paper, we analyze two well-known boosting methods, AdaBoost and Incremental Forward Stagewise Regression (FS$_\varepsilon$), by establishing their precise connections to the Mirror Descent algorithm, which is a first-order method in convex optimization. As a consequence of these connections we obtain novel computational guarantees for these boosting methods. In particular, we characterize convergence bounds of AdaBoost, related to both the margin and log-exponential loss function, for any step-size sequence. Furthermore, this paper presents, for the first time, precise computational complexity results for FS$_\varepsilon$.

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Robert M. Freund, Paul Grigas, Rahul Mazumder. 2013-07-04. AdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods. https://arxiv.org/abs/1307.1192

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