  Federated learning (FL), as a type of collaborative machine learning
framework, is capable of preserving private data from mobile terminals (MTs)
while training the data into useful models. Nevertheless, from a viewpoint of
information theory, it is still possible for a curious server to infer private
information from the shared models uploaded by MTs. To address this problem, we
first make use of the concept of local differential privacy (LDP), and propose
a user-level differential privacy (UDP) algorithm by adding artificial noise to
the shared models before uploading them to servers. According to our analysis,
the UDP framework can realize $(\epsilon_{i}, \delta_{i})$-LDP for the $i$-th
MT with adjustable privacy protection levels by varying the variances of the
artificial noise processes. We then derive a theoretical convergence
upper-bound for the UDP algorithm. It reveals that there exists an optimal
number of communication rounds to achieve the best learning performance. More
importantly, we propose a communication rounds discounting (CRD) method.
Compared with the heuristic search method, the proposed CRD method can achieve
a much better trade-off between the computational complexity of searching and
the convergence performance. Extensive experiments indicate that our UDP
algorithm using the proposed CRD method can effectively improve both the
training efficiency and model quality for the given privacy protection levels.
