  In this work, we propose a new optimization framework for multiclass boosting
learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two
successful multiclass boosting algorithms, which can use binary weak learners.
We explicitly derive these two algorithms' Lagrange dual problems based on
their regularized loss functions. We show that the Lagrange dual formulations
enable us to design totally-corrective multiclass algorithms by using the
primal-dual optimization technique. Experiments on benchmark data sets suggest
that our multiclass boosting can achieve a comparable generalization capability
with state-of-the-art, but the convergence speed is much faster than stage-wise
gradient descent boosting. In other words, the new totally corrective
algorithms can maximize the margin more aggressively.
