  The increasing reliance on ML models in high-stakes tasks has raised a major
concern on fairness violations. Although there has been a surge of work that
improves algorithmic fairness, most of them are under the assumption of an
identical training and test distribution. In many real-world applications,
however, such an assumption is often violated as previously trained fair models
are often deployed in a different environment, and the fairness of such models
has been observed to collapse. In this paper, we study how to transfer model
fairness under distribution shifts, a widespread issue in practice. We conduct
a fine-grained analysis of how the fair model is affected under different types
of distribution shifts and find that domain shifts are more challenging than
subpopulation shifts. Inspired by the success of self-training in transferring
accuracy under domain shifts, we derive a sufficient condition for transferring
group fairness. Guided by it, we propose a practical algorithm with a fair
consistency regularization as the key component. A synthetic dataset benchmark,
which covers all types of distribution shifts, is deployed for experimental
verification of the theoretical findings. Experiments on synthetic and real
datasets including image and tabular data demonstrate that our approach
effectively transfers fairness and accuracy under various distribution shifts.
