  A fundamental challenge for machine learning models is how to generalize
learned models for out-of-distribution (OOD) data. Among various approaches,
exploiting invariant features by Domain Adversarial Training (DAT) received
widespread attention. Despite its success, we observe training instability from
DAT, mostly due to over-confident domain discriminator and environment label
noise. To address this issue, we proposed Environment Label Smoothing (ELS),
which encourages the discriminator to output soft probability, which thus
reduces the confidence of the discriminator and alleviates the impact of noisy
environment labels. We demonstrate, both experimentally and theoretically, that
ELS can improve training stability, local convergence, and robustness to noisy
environment labels. By incorporating ELS with DAT methods, we are able to yield
state-of-art results on a wide range of domain generalization/adaptation tasks,
particularly when the environment labels are highly noisy.
