In this paper, to effectively prevent the differential attack, we propose a novel Federated learning (FL) framework based on the concept of differential privacy (DP), in which artificial noises are added to the parameters at the clients side before being uploaded for aggregating, namely, noising before model aggregation FL (NbAFL). First, we prove that the NbAFL can satisfy DP under distinct protection levels by properly adapting the variances of artificial noises. Then we develop a theoretical convergence bound of the loss function of the trained FL model in the NbAFL. Our developed bound reveals the following three key properties: 1) There is a tradeoff between the convergence performance and privacy protection levels, i.e., a better convergence performance leads to a lower protection level; 2) Increasing the number $N$ of overall clients participating in FL can improve the convergence performance, given a fixed privacy protection level; 3) There is an optimal number of maximum aggregation times in terms of convergence performance for a given protection level. Furthermore, we propose a $K$-random scheduling strategy, where $K$ ($1<K<N$) clients are randomly selected from the $N$ overall clients to participate in each aggregation. We also develop the corresponding convergence bound of the loss function in this case. From our analysis, the $K$-random scheduling strategy can retain the above three properties. More interestingly, we find that there is an optimal $K$ that achieves the best convergence performance at a fixed privacy level. Evaluations demonstrate that our theoretical results are consistent with simulations, thereby facilitating the designs on various privacy-preserving FL algorithms with different tradeoff requirements on convergence performance and privacy levels.

采用微分隐私概念，提出一种在模型聚合之前加入人工噪音的差分隐私框架，证明该框架可以在不同保护级别下满足差分隐私。同时，优化了聚合轮数、系统总参与用户数和随机选取的用户数，实现了在不同隐私保护和性能要求下的隐私保护联邦学习算法设计，并通过仿真实验证明了该理论的正确性。

差分隐私联邦学习算法及性能分析