  This manuscript provides optimization guarantees, generalization bounds, and
statistical consistency results for AdaBoost variants which replace the
exponential loss with the logistic and similar losses (specifically, twice
differentiable convex losses which are Lipschitz and tend to zero on one side).
  The heart of the analysis is to show that, in lieu of explicit regularization
and constraints, the structure of the problem is fairly rigidly controlled by
the source distribution itself. The first control of this type is in the
separable case, where a distribution-dependent relaxed weak learning rate
induces speedy convergence with high probability over any sample. Otherwise, in
the nonseparable case, the convex surrogate risk itself exhibits
distribution-dependent levels of curvature, and consequently the algorithm's
output has small norm with high probability.
