Privacy-Preserving Federated Learning for Digital Libraries Quarterly Focus in Uganda: Robustness Under Distribution Shift and Sparse Labels

Federated learning offers a promising architecture for digital library consortia in low-resource settings, where centralising user interaction data is often infeasible due to privacy concerns and bandwidth constraints. We introduce a client-weighted aggregation rule that corrects for covariate shift through importance re-weighting, and we propose a semi-supervised local update mechanism that leverages unlabelled query logs to stabilise training when labelled relevance data are scarce. Formal convergence guarantees are established under mild assumptions on client heterogeneity, and a communication-efficient variant is derived using gradient compression with error feedback. The framework is presented as a methodological contribution, with explicit attention to the infrastructural constraints of the Ugandan context, including intermittent connectivity and limited computational capacity. We argue that robustness to distribution shift and label sparsity must be designed jointly rather than treated as separate concerns, and we identify the specific conditions under which the proposed methods are theoretically justified.