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  1. In distributed machine learning, while a great deal of attention has been paid on centralized systems that include a central parameter server, decentralized systems have not been fully explored. Decentralized systems have great potentials in the future practical use as they have multiple useful attributes such as less vulnerable to privacy and security issues, better scalability, and less prone to single point of bottleneck and failure. In this paper, we focus on decentralized learning systems and aim to achieve differential privacy with good convergence rate and low communication cost. To achieve this goal, we propose a new algorithm, Leader-Follower Elastic Averaging Stochastic Gradient Descent (LEASGD), driven by a novel Leader-Follower topology and differential privacy model. We also provide a theoretical analysis of the convergence rate of LEASGD and the trade-off between the performance and privacy in the private setting. We evaluate LEASGD in real distributed testbed with poplar deep neural network models MNIST-CNN, MNIST-RNN, and CIFAR-10. Extensive experimental results show that LEASGD outperforms state-of-the-art decentralized learning algorithm DPSGD by achieving nearly 40% lower loss function within same iterations and by 30% reduction of communication cost. Moreover, it spends less differential privacy budget and has final higher accuracy result than DPSGD under private setting. 
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