BibTeX
@MISC{Telgarsky_thefast,
author = {Matus Telgarsky},
title = {The Fast Convergence of Boosting},
year = {}
}
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Abstract
This manuscript considers the convergence rate of boosting under a large class of losses, including the exponential and logistic losses, where the best previous rate of convergence was O(exp(1/ɛ 2)). First, it is established that the setting of weak learnability aids the entire class, granting a rate O(ln(1/ɛ)). Next, the (disjoint) conditions under which the infimal empirical risk is attainable are characterized in terms of the sample and weak learning class, and a new proof is given for the known rate O(ln(1/ɛ)). Finally, it is established that any instance can be decomposed into two smaller instances resembling the two preceding special cases, yielding a rate O(1/ɛ), with a matching lower bound for the logistic loss. The principal technical hurdle throughout this work is the potential unattainability of the infimal empirical risk; the technique for overcoming this barrier may be of general interest. 1
