Convergence Analysis and Optimisation of Privacy-Preserving Federated Learning for Hierarchical Graph Neural Networks in Distributed Cloud Anomaly Detection

Distributed cloud networks spanning multiple jurisdictions face significant challenges in anomaly detection due to privacy constraints, regulatory requirements, and communication limitations. This paper presents a mathematically rigorous framework for privacy-preserving federated learning on hierarchical graph neural networks, providing theoretical convergence guarantees and optimisation bounds for distributed anomaly detection. A novel layer-wise federated aggregation mechanism is introduced, featuring a proven convergence rate O1/T. That preserves hierarchical structure during distributed training. The theoretical analysis establishes differential privacy guarantees of ε=1.0, δ=10−5 through layer-specific noise calibration, achieving optimal privacy–utility tradeoffs. The proposed optimisation framework incorporates: (1) convergence-guaranteed layer-wise aggregation with bounded gradient norms, (2) privacy-preserving mechanisms with formal composition analysis under the Moments Accountant framework, (3) meta-learning-based personalisation with theoretical generalisation bounds, and (4) communication-efficient protocols with a proven 93% reduction in overhead. Rigorous evaluation on the FEDGEN testbed, spanning 2780 km across Nigeria and the Democratic Republic of Congo, demonstrates superior performance with hierarchical F1-scores exceeding 95% across all regions, while maintaining theoretical guarantees. The framework’s convergence analysis shows robustness under realistic constraints, including 67% client participation, 200 ms latency, and 20 Mbps bandwidth limitations. This work advances the theoretical foundations of federated graph learning while providing practical deployment guidelines for cross-jurisdictional cloud networks.