  Federated learning (FL) enables distributed clients to collaboratively train
a machine learning model without sharing raw data with each other. However, it
suffers the leakage of private information from uploading models. In addition,
as the model size grows, the training latency increases due to limited
transmission bandwidth and the model performance degrades while using
differential privacy (DP) protection. In this paper, we propose a gradient
sparsification empowered FL framework over wireless channels, in order to
improve training efficiency without sacrificing convergence performance.
Specifically, we first design a random sparsification algorithm to retain a
fraction of the gradient elements in each client's local training, thereby
mitigating the performance degradation induced by DP and and reducing the
number of transmission parameters over wireless channels. Then, we analyze the
convergence bound of the proposed algorithm, by modeling a non-convex FL
problem. Next, we formulate a time-sequential stochastic optimization problem
for minimizing the developed convergence bound, under the constraints of
transmit power, the average transmitting delay, as well as the client's DP
requirement. Utilizing the Lyapunov drift-plus-penalty framework, we develop an
analytical solution to the optimization problem. Extensive experiments have
been implemented on three real life datasets to demonstrate the effectiveness
of our proposed algorithm. We show that our proposed algorithms can fully
exploit the interworking between communication and computation to outperform
the baselines, i.e., random scheduling, round robin and delay-minimization
algorithms.
