  While preserving the privacy of federated learning (FL), differential privacy
(DP) inevitably degrades the utility (i.e., accuracy) of FL due to model
perturbations caused by DP noise added to model updates. Existing studies have
considered exclusively noise with persistent root-mean-square amplitude and
overlooked an opportunity of adjusting the amplitudes to alleviate the adverse
effects of the noise. This paper presents a new DP perturbation mechanism with
a time-varying noise amplitude to protect the privacy of FL and retain the
capability of adjusting the learning performance. Specifically, we propose a
geometric series form for the noise amplitude and reveal analytically the
dependence of the series on the number of global aggregations and the
$(\epsilon,\delta)$-DP requirement. We derive an online refinement of the
series to prevent FL from premature convergence resulting from excessive
perturbation noise. Another important aspect is an upper bound developed for
the loss function of a multi-layer perceptron (MLP) trained by FL running the
new DP mechanism. Accordingly, the optimal number of global aggregations is
obtained, balancing the learning and privacy. Extensive experiments are
conducted using MLP, supporting vector machine, and convolutional neural
network models on four public datasets. The contribution of the new DP
mechanism to the convergence and accuracy of privacy-preserving FL is
corroborated, compared to the state-of-the-art Gaussian noise mechanism with a
persistent noise amplitude.
