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. In this work, we propose \underline{H}ierarchical \underline{F}ederated Learning with \underline{H}ierarchical \underline{D}ifferential \underline{P}rivacy ({\tt H$^2$FDP}), a DP-enhanced FL methodology for jointly optimizing privacy and performance in hierarchical networks. Building upon recent proposals for Hierarchical Differential Privacy (HDP), one of the key concepts of {\tt H$^2$FDP} is adapting DP noise injection at different layers of an established FL hierarchy -- edge devices, edge servers, and cloud servers -- according to the trust models within particular subnetworks. We conduct a comprehensive analysis of the convergence behavior of {\tt H$^2$FDP}, 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. Leveraging these relationships, we develop an adaptive control algorithm for {\tt H$^2$FDP} that tunes properties of local model training to minimize communication energy, latency, and the stationarity gap while striving to maintain a sub-linear convergence rate and meet desired privacy criteria. Subsequent numerical evaluations demonstrate that {\tt H$^2$FDP} obtains substantial improvements in these metrics over baselines for different privacy budgets, and validate the impact of different system configurations.

翻译：尽管联邦学习（FL）消除了原始数据在网络中的传输，但其通信的模型参数仍易遭受隐私泄露。本文提出一种名为\underline{层次化}联邦学习与\underline{层次化}差分\underline{隐私}（{\tt H$^2$FDP}）的DP增强型FL方法，旨在层次化网络中联合优化隐私与性能。基于近期提出的层次化差分隐私（HDP）方法，{\tt H$^2$FDP}的核心思想是根据特定子网络内的信任模型，在已建立的FL层次结构（边缘设备、边缘服务器和云服务器）的不同层级自适应地注入DP噪声。我们对{\tt H$^2$FDP}的收敛行为进行了全面分析，揭示了参数调优的条件：当满足这些条件时，训练过程会以次线性速度收敛至一个有限平稳性间隙，该间隙取决于网络层次结构、信任模型及目标隐私等级。基于上述关系，我们开发了{\tt H$^2$FDP}的自适应控制算法，通过调整局部模型训练参数来最小化通信能耗、延迟和平稳性间隙，同时尽力维持次线性收敛速度并满足期望的隐私准则。数值评估结果表明，在不同隐私预算下，{\tt H$^2$FDP}相较于基线方法在上述指标上取得了显著提升，并验证了不同系统配置的影响。