In this paper, to effectively prevent information leakage, we propose a novel
framework based on the concept of differential privacy (DP), in which
artificial noises are added to the parameters at the clients side before
aggregating, namely, noising before model aggregation FL (NbAFL). First, we
prove that the NbAFL can satisfy DP under distinct protection levels by
properly adapting different variances of artificial noises. Then we develop a
theoretical convergence bound of the loss function of the trained FL model in
the NbAFL. Specifically, the theoretical 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) Given a fixed privacy protection level, increasing
the number $N$ of overall clients participating in FL can improve the
convergence performance; 3) There is an optimal number of maximum aggregation
times (communication rounds) 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 and the $K$-random
scheduling strategy can also retain the above three properties. Moreover, 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。