  Distributional robustness is a promising framework for training deep learning
models that are less vulnerable to adversarial examples and data distribution
shifts. Previous works have mainly focused on exploiting distributional
robustness in the data space. In this work, we explore an optimal
transport-based distributional robustness framework in model spaces.
Specifically, we examine a model distribution within a Wasserstein ball
centered on a given model distribution that maximizes the loss. We have
developed theories that enable us to learn the optimal robust center model
distribution. Interestingly, our developed theories allow us to flexibly
incorporate the concept of sharpness awareness into training, whether it's a
single model, ensemble models, or Bayesian Neural Networks, by considering
specific forms of the center model distribution. These forms include a Dirac
delta distribution over a single model, a uniform distribution over several
models, and a general Bayesian Neural Network. Furthermore, we demonstrate that
Sharpness-Aware Minimization (SAM) is a specific case of our framework when
using a Dirac delta distribution over a single model, while our framework can
be seen as a probabilistic extension of SAM. To validate the effectiveness of
our framework in the aforementioned settings, we conducted extensive
experiments, and the results reveal remarkable improvements compared to the
baselines.
