  The endeavor to preserve the generalization of a fair and invariant
classifier across domains, especially in the presence of distribution shifts,
becomes a significant and intricate challenge in machine learning. In response
to this challenge, numerous effective algorithms have been developed with a
focus on addressing the problem of fairness-aware domain generalization. These
algorithms are designed to navigate various types of distribution shifts, with
a particular emphasis on covariate and dependence shifts. In this context,
covariate shift pertains to changes in the marginal distribution of input
features, while dependence shift involves alterations in the joint distribution
of the label variable and sensitive attributes. In this paper, we introduce a
simple but effective approach that aims to learn a fair and invariant
classifier by simultaneously addressing both covariate and dependence shifts
across domains. We assert the existence of an underlying transformation model
can transform data from one domain to another, while preserving the semantics
related to non-sensitive attributes and classes. By augmenting various
synthetic data domains through the model, we learn a fair and invariant
classifier in source domains. This classifier can then be generalized to
unknown target domains, maintaining both model prediction and fairness
concerns. Extensive empirical studies on four benchmark datasets demonstrate
that our approach surpasses state-of-the-art methods.
