This paper develops a networked federated learning algorithm to solve nonsmooth objective functions. To guarantee the confidentiality of the participants with respect to each other and potential eavesdroppers, we use the zero-concentrated differential privacy notion (zCDP). Privacy is achieved by perturbing the outcome of the computation at each client with a variance-decreasing Gaussian noise. ZCDP allows for better accuracy than the conventional $(\epsilon, \delta)$-DP and stronger guarantees than the more recent R\'enyi-DP by assuming adversaries aggregate all the exchanged messages. The proposed algorithm relies on the distributed Alternating Direction Method of Multipliers (ADMM) and uses the approximation of the augmented Lagrangian to handle nonsmooth objective functions. The developed private networked federated learning algorithm has a competitive privacy accuracy trade-off and handles nonsmooth and non-strongly convex problems. We provide complete theoretical proof for the privacy guarantees and the algorithm's convergence to the exact solution. We also prove under additional assumptions that the algorithm converges in $O(1/n)$ ADMM iterations. Finally, we observe the performance of the algorithm in a series of numerical simulations.

翻译：本文开发了一种网络化联邦学习算法，用于求解非光滑目标函数。为确保参与者之间及针对潜在窃听者的机密性，我们采用了零集中差分隐私概念(zCDP)。隐私保护通过对每个客户端的计算结果添加方差递减的高斯噪声来实现。相比传统的$(\epsilon, \delta)$-DP，zCDP能实现更高的准确度，且相较于更新的Rényi-DP，它通过假设攻击者聚合所有交换消息而提供更强保障。所提算法基于分布式交替方向乘子法(ADMM)，并利用增广拉格朗日函数的逼近来处理非光滑目标函数。该私有网络化联邦学习算法具有竞争性的隐私-准确度权衡，并能处理非光滑与非强凸问题。我们提供了关于隐私保障及算法收敛到精确解的完整理论证明。同时在附加假设下证明了算法在$O(1/n)$次ADMM迭代后收敛。最后通过一系列数值模拟观察了算法的性能表现。