Privacy-Preserving Federated Learning for Container Kubernetes Orchestration in Uganda: Robustness Under Distribution Shift and Sparse Labels

Federated learning offers a compelling architecture for training machine learning models across distributed Kubernetes clusters without centralising sensitive data, yet its practical deployment in resource-constrained settings such as Uganda confronts two interrelated obstacles that current literature treats in isolation: distribution shift between participating sites and extreme label sparsity. We introduce a hierarchical Bayesian model of client heterogeneity that distinguishes benign statistical variation from systematic covariate shift, and we prove that a proposed double-regularised aggregation operator achieves bounded excess risk under conditions where standard FedAvg diverges. The framework further incorporates a semi-supervised pseudo-labelling mechanism with rigorous uncertainty thresholds, demonstrating that selective label propagation can stabilise training when annotated data are scarce. Theoretical analysis establishes convergence guarantees under non-IID data partitions, and the architectural instantiation on Kubernetes demonstrates that privacy constraints, implemented through secure aggregation and differential privacy, do not compromise the robustness properties we derive. The contribution is a unified treatment of distribution shift and label scarcity that yields testable propositions for deployment in Ugandan data centres and other low-resource environments.