Federated Learning (FL) enables decentralized model training on edge devices without sharing raw data, ensuring data privacy. However, most existing aggregation methods such as FedAvg, FedProx, FedNova, AFL, and SCAFFOLD rely on simple averaging or linear weighting of client updates. These approaches perform well in homogeneous settings but become ineffective under heterogeneous data distributions, where large variations in client gradients cause unstable global updates and reduced robustness. To address this limitation, this paper proposes a novel aggregation framework named FedLag, which employs statistical modeling for more reliable global update fusion. FedLag constructs Gaussian representations of client gradient distributions to identify Lagrangian points that capture stable regions between conflicting updates. For each model parameter, the server evaluates weighted likelihood functions based on client dataset sizes and selects the gradient with the highest likelihood as the global update. Although comprehensive experimental validation is beyond the scope of this paper, the proposed method is theoretically shown to be more robust against noise and outliers. By integrating probabilistic modeling with likelihood-based selection, FedLag provides an innovative and resilient aggregation strategy for heterogeneous Federated Learning environments.
Manikandan et al. (2026) studied this question.