Differentially private distributed online learning over time-varying digraphs via dual averaging

This article investigates a distributed online learning problem with privacy preservation, in which the learning nodes in a distributed network aims to minimize the sum of local loss functions over time horizon (Formula presented.). Based on the push-sum protocol and the Laplace mechanism, we propose a differentially private distributed dual averaging algorithm for constrained distributed online learning problem over time-varying digraphs. It is shown that the expectation of the regret of our algorithm achieves a sublinear rate of (Formula presented.). Furthermore, we provide an analysis of differential privacy, which reveals a tradeoff between the accuracy and the privacy level of our algorithm. Finally, numerical examples are presented to validate the effectiveness of the algorithm.