  We present a new online boosting algorithm for adapting the weights of a
boosted classifier, which yields a closer approximation to Freund and
Schapire's AdaBoost algorithm than previous online boosting algorithms. We also
contribute a new way of deriving the online algorithm that ties together
previous online boosting work. We assume that the weak hypotheses were selected
beforehand, and only their weights are updated during online boosting. The
update rule is derived by minimizing AdaBoost's loss when viewed in an
incremental form. The equations show that optimization is computationally
expensive. However, a fast online approximation is possible. We compare
approximation error to batch AdaBoost on synthetic datasets and generalization
error on face datasets and the MNIST dataset.
