  Boosting is a generic learning method for classification and regression. Yet,
as the number of base hypotheses becomes larger, boosting can lead to a
deterioration of test performance. Overfitting is an important and ubiquitous
phenomenon, especially in regression settings. To avoid overfitting, we
consider using $l_1$ regularization. We propose a novel Frank-Wolfe type
boosting algorithm (FWBoost) applied to general loss functions. By using
exponential loss, the FWBoost algorithm can be rewritten as a variant of
AdaBoost for binary classification. FWBoost algorithms have exactly the same
form as existing boosting methods, in terms of making calls to a base learning
algorithm with different weights update. This direct connection between
boosting and Frank-Wolfe yields a new algorithm that is as practical as
existing boosting methods but with new guarantees and rates of convergence.
Experimental results show that the test performance of FWBoost is not degraded
with larger rounds in boosting, which is consistent with the theoretical
analysis.
