Out-of-Distribution Generalization of Federated Learning via Implicit Invariant Relationships

Out-of-distribution generalization is challenging for non-participating clients of federated learning under distribution shifts. A proven strategy is to explore those invariant relationships between input and target variables, working equally well for non-participating clients. However, learning invariant relationships is often in an explicit manner from data, representation, and distribution, which violates the federated principles of privacypreserving and limited communication. In this paper, we propose FEDIIR, which implicitly learns invariant relationships from parameter for out-ofdistribution generalization, adhering to the above principles. Specifically, we utilize the prediction disagreement to quantify invariant relationships and implicitly reduce it through inter-client gradient alignment. Theoretically, we demonstrate the range of non-participating clients to which FEDIIR is expected to generalize and present the convergence results for FEDIIR in the massively distributed with limited communication. Extensive experiments show that FEDIIR significantly outperforms relevant baselines in terms of out-ofdistribution generalization of federated learning.