The Convergence Rate of AdaBoost and Friends

The worst case convergence rate of AdaBoost, and of a family of related optimization problems including LogitBoost, is $\mathcal O(1/\epsilon)$, where the hidden terms depend on the loss function, the weak learning class, and the sample. In certain situations, the rate is $\mathcal O(\ln(1/\epsilon))$. Lastly, Schapire's example of slow convergence has rate $\Omega(1/\epsilon)$, however the hidden terms are not tight with the upper bound.