  This paper addresses intra-client and inter-client covariate shifts in
federated learning (FL) with a focus on the overall generalization performance.
To handle covariate shifts, we formulate a new global model training paradigm
and propose Federated Importance-Weighted Empirical Risk Minimization (FTW-ERM)
along with improving density ratio matching methods without requiring perfect
knowledge of the supremum over true ratios. We also propose the
communication-efficient variant FITW-ERM with the same level of privacy
guarantees as those of classical ERM in FL. We theoretically show that FTW-ERM
achieves smaller generalization error than classical ERM under certain
settings. Experimental results demonstrate the superiority of FTW-ERM over
existing FL baselines in challenging imbalanced federated settings in terms of
data distribution shifts across clients.
