  In this paper, we present the Bennett-type generalization bounds of the
learning process for i.i.d. samples, and then show that the generalization
bounds have a faster rate of convergence than the traditional results. In
particular, we first develop two types of Bennett-type deviation inequality for
the i.i.d. learning process: one provides the generalization bounds based on
the uniform entropy number; the other leads to the bounds based on the
Rademacher complexity. We then adopt a new method to obtain the alternative
expressions of the Bennett-type generalization bounds, which imply that the
bounds have a faster rate o(N^{-1/2}) of convergence than the traditional
results O(N^{-1/2}). Additionally, we find that the rate of the bounds will
become faster in the large-deviation case, which refers to a situation where
the empirical risk is far away from (at least not close to) the expected risk.
Finally, we analyze the asymptotical convergence of the learning process and
compare our analysis with the existing results.
