Finding lost DG: Explaining domain generalization via model complexity

The domain generalization (DG) problem setting challenges a model trained on multiple known data distributions to generalise well on unseen data distributions. Due to its practical importance, a large number of methods have been proposed to address this challenge. However much of the work in general purpose DG is heuristically motivated, as the DG problem is hard to model formally; and recent evaluations have cast doubt on existing methods' practical efficacy -- in particular compared to a well tuned empirical risk minimisation baseline. We present a novel learning-theoretic generalisation bound for DG that bounds unseen domain generalisation performance in terms of the model's Rademacher complexity. Based on this, we conjecture that existing methods' efficacy or lack thereof is largely determined by an empirical risk vs predictor complexity trade-off, and demonstrate that their performance variability can be explained in these terms. Algorithmically, this analysis suggests that domain generalisation should be achieved by simply performing regularised ERM with a leave-one-domain-out cross-validation objective. Empirical results on the DomainBed benchmark corroborate this.