Objective Mismatch in Federated Learning under Missing Class Support

Federated learning (FL) often assumes that all classes are observed across clients. However, in many real-world applications such as fall detection, a large fraction of clients contain no samples of rare but critical events. We show that this leads to a fundamental failure mode, where FL appears to converge while remaining biased on rare classes. We theoretically prove that this induces an irreducible bias that cannot be eliminated by longer training or local reweighting. To mitigate this issue, we propose a simple server-side correction and demonstrate its effectiveness on both synthetic data and a real-world dataset.