  Federated learning is a distributed machine learning approach which enables a
shared server model to learn by aggregating the locally-computed parameter
updates with the training data from spatially-distributed client silos. Though
successfully possessing advantages in both scale and privacy, federated
learning is hurt by domain shift problems, where the learning models are unable
to generalize to unseen domains whose data distribution is non-i.i.d. with
respect to the training domains. In this study, we propose the Federated
Invariant Learning Consistency (FedILC) approach, which leverages the gradient
covariance and the geometric mean of Hessians to capture both inter-silo and
intra-silo consistencies of environments and unravel the domain shift problems
in federated networks. The benchmark and real-world dataset experiments bring
evidence that our proposed algorithm outperforms conventional baselines and
similar federated learning algorithms. This is relevant to various fields such
as medical healthcare, computer vision, and the Internet of Things (IoT). The
code is released at https://github.com/mikemikezhu/FedILC.
