  This paper provides a general result on controlling local Rademacher
complexities, which captures in an elegant form to relate the complexities with
constraint on the expected norm to the corresponding ones with constraint on
the empirical norm. This result is convenient to apply in real applications and
could yield refined local Rademacher complexity bounds for function classes
satisfying general entropy conditions. We demonstrate the power of our
complexity bounds by applying them to derive effective generalization error
bounds.
