  Regularization of Deep Neural Networks (DNNs) for the sake of improving their
generalization capability is important and challenging. The development in this
line benefits theoretical foundation of DNNs and promotes their usability in
different areas of artificial intelligence. In this paper, we investigate the
role of Rademacher complexity in improving generalization of DNNs and propose a
novel regularizer rooted in Local Rademacher Complexity (LRC). While Rademacher
complexity is well known as a distribution-free complexity measure of function
class that help boost generalization of statistical learning methods, extensive
study shows that LRC, its counterpart focusing on a restricted function class,
leads to sharper convergence rates and potential better generalization given
finite training sample. Our LRC based regularizer is developed by estimating
the complexity of the function class centered at the minimizer of the empirical
loss of DNNs. Experiments on various types of network architecture demonstrate
the effectiveness of LRC regularization in improving generalization. Moreover,
our method features the state-of-the-art result on the CIFAR-$10$ dataset with
network architecture found by neural architecture search.
