  Distributed learning systems have enabled training large-scale models over
large amount of data in significantly shorter time. In this paper, we focus on
decentralized distributed deep learning systems and aim to achieve differential
privacy with good convergence rate and low communication cost. To achieve this
goal, we propose a new learning algorithm LEASGD (Leader-Follower Elastic
Averaging Stochastic Gradient Descent), which is driven by a novel
Leader-Follower topology and a differential privacy model.We provide a
theoretical analysis of the convergence rate and the trade-off between the
performance and privacy in the private setting.The experimental results show
that LEASGD outperforms state-of-the-art decentralized learning algorithm DPSGD
by achieving steadily lower loss within the same iterations and by reducing the
communication cost by 30%. In addition, LEASGD spends less differential privacy
budget and has higher final accuracy result than DPSGD under private setting.
