In spite that Federated Learning (FL) is well known for its privacy
protection when training machine learning models among distributed clients
collaboratively, recent studies have pointed out that the naive FL is
susceptible to gradient leakage attacks. In the meanwhile, Differential Privacy
(DP) emerges as a promising countermeasure to defend against gradient leakage
attacks. However, the adoption of DP by clients in FL may significantly
jeopardize the model accuracy. It is still an open problem to understand the
practicality of DP from a theoretic perspective. In this paper, we make the
first attempt to understand the practicality of DP in FL through tuning the
number of conducted iterations. Based on the FedAvg algorithm, we formally
derive the convergence rate with DP noises in FL. Then, we theoretically
derive: 1) the conditions for the DP based FedAvg to converge as the number of
global iterations (GI) approaches infinity; 2) the method to set the number of
local iterations (LI) to minimize the negative influence of DP noises. By
further substituting the Laplace and Gaussian mechanisms into the derived
convergence rate respectively, we show that: 3) The DP based FedAvg with the
Laplace mechanism cannot converge, but the divergence rate can be effectively
prohibited by setting the number of LIs with our method; 4) The learning error
of the DP based FedAvg with the Gaussian mechanism can converge to a constant
number finally if we use a fixed number of LIs per GI. To verify our
theoretical findings, we conduct extensive experiments using two real-world
datasets. The results not only validate our analysis results, but also provide
useful guidelines on how to optimize model accuracy when incorporating DP into

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