Understanding Generalization in Client-Level DP-FL: A Hierarchical Stability Analysis

Differentially private federated learning (DP-FL) has been extensively studied for privacy and optimization, while its generalization remains less understood. Since data in FL are organized at the client and local-sample levels, they give rise to within-client and unseen-client generalization. We develop a hierarchical distributional-stability framework for client-level DP-FL based on sample- and client-replacement stability, revealing that the heterogeneity term explicitly enters the unseen-client generalization bound, whereas local dataset size explicitly governs the within-client generalization bound. Using total variation (TV) distance and KL divergence, we derive complementary generalization guarantees: the TV-based bound exhibits a tighter dependence on the client participation ratio, whereas the KL-based bound exhibits a tighter dependence on the training horizon. Furthermore, under suitable learning-rate decay, the KL-based bound can remain independent of the training horizon without requiring a finite cumulative step size. Combining these generalization guarantees with optimization analysis, we derive population excess-risk bounds that characterize the optimization-generalization trade-off induced by privacy, training dynamics, and heterogeneity. Experiments across multiple datasets empirically support the hierarchical decomposition and the main theoretical predictions.