  Machine learning systems typically assume that the distributions of training
and test sets match closely. However, a critical requirement of such systems in
the real world is their ability to generalize to unseen domains. Here, we
propose an inter-domain gradient matching objective that targets domain
generalization by maximizing the inner product between gradients from different
domains. Since direct optimization of the gradient inner product can be
computationally prohibitive -- requires computation of second-order derivatives
-- we derive a simpler first-order algorithm named Fish that approximates its
optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds
benchmark, which captures distribution shift across a diverse range of
modalities. Our method produces competitive results on these datasets and
surpasses all baselines on 4 of them. We perform experiments on both the Wilds
benchmark, which captures distribution shift in the real world, as well as
datasets in DomainBed benchmark that focuses more on synthetic-to-real
transfer. Our method produces competitive results on both benchmarks,
demonstrating its effectiveness across a wide range of domain generalization
tasks.

Machine Learning;Machine Learning