  Stability analysis is an essential aspect of studying the generalization
ability of deep learning, as it involves deriving generalization bounds for
stochastic gradient descent-based training algorithms. Adversarial training is
the most widely used defense against adversarial example attacks. However,
previous generalization bounds for adversarial training have not included
information regarding the data distribution. In this paper, we fill this gap by
providing generalization bounds for stochastic gradient descent-based
adversarial training that incorporate data distribution information. We utilize
the concepts of on-average stability and high-order approximate Lipschitz
conditions to examine how changes in data distribution and adversarial budget
can affect robust generalization gaps. Our derived generalization bounds for
both convex and non-convex losses are at least as good as the uniform
stability-based counterparts which do not include data distribution
information. Furthermore, our findings demonstrate how distribution shifts from
data poisoning attacks can impact robust generalization.
