  A crucial aspect in reliable machine learning is to design a deployable
system in generalizing new related but unobserved environments. Domain
generalization aims to alleviate such a prediction gap between the observed and
unseen environments. Previous approaches commonly incorporated learning
invariant representation for achieving good empirical performance. In this
paper, we reveal that merely learning invariant representation is vulnerable to
the unseen environment. To this end, we derive novel theoretical analysis to
control the unseen test environment error in the representation learning, which
highlights the importance of controlling the smoothness of representation. In
practice, our analysis further inspires an efficient regularization method to
improve the robustness in domain generalization. Our regularization is
orthogonal to and can be straightforwardly adopted in existing domain
generalization algorithms for invariant representation learning. Empirical
results show that our algorithm outperforms the base versions in various
dataset and invariance criteria.
