Differentially-Private Multi-Tier Federated Learning: A Formal Analysis and Evaluation

While federated learning (FL) eliminates the transmission of raw data over a network, it is still vulnerable to privacy breaches from the communicated model parameters. Differential privacy (DP) is often employed to address such issues. However, the impact of DP on FL in multi-tier networks -- where hierarchical aggregations couple noise injection decisions at different tiers, and trust models are heterogeneous across subnetworks -- is not well understood. To fill this gap, we develop underlineMulti-Tier underlineFederated Learning with underlineMulti-Tier underlineDifferential underlinePrivacy (tt M2FDP), a DP-enhanced FL methodology for jointly optimizing privacy and performance over such networks. One of the key principles of tt M2FDP is to adapt DP noise injection across the established edge/fog computing hierarchy (e.g., edge devices, intermediate nodes, and other tiers up to cloud servers) according to the trust models in different subnetworks. We conduct a comprehensive analysis of the convergence behavior of tt M2FDP under non-convex problem settings, revealing conditions on parameter tuning under which the training process converges sublinearly to a finite stationarity gap that depends on the network hierarchy, trust model, and target privacy level. We show how these relationships can be employed to develop an adaptive control algorithm for tt M2FDP that tunes properties of local model training to minimize energy, latency, and the stationarity gap while meeting desired convergence and privacy criterion. Subsequent numerical evaluations demonstrate that tt M2FDP obtains substantial improvements in these metrics over baselines for different privacy budgets and system configurations.