  The ability to generalize to unseen domains is crucial for machine learning
systems deployed in the real world, especially when we only have data from
limited training domains. In this paper, we propose a simple and effective
regularization method based on the nuclear norm of the learned features for
domain generalization. Intuitively, the proposed regularizer mitigates the
impacts of environmental features and encourages learning domain-invariant
features. Theoretically, we provide insights into why nuclear norm
regularization is more effective compared to ERM and alternative regularization
methods. Empirically, we conduct extensive experiments on both synthetic and
real datasets. We show nuclear norm regularization achieves strong performance
compared to baselines in a wide range of domain generalization tasks. Moreover,
our regularizer is broadly applicable with various methods such as ERM and SWAD
with consistently improved performance, e.g., 1.7% and 0.9% test accuracy
improvements respectively on the DomainBed benchmark.
