In the big data era, the generation of data presents some new characteristics, including wide distribution, high velocity, high dimensionality, and privacy concern. To address these challenges for big data analytics, we develop a privacy-preserving distributed online learning framework on the data collected from distributed data sources. Specifically, each node (i.e., data source) has the capacity of learning a model from its local dataset, and exchanges intermediate parameters with a random part of their own neighboring (logically connected) nodes. Hence, the topology of the communications in our distributed computing framework is unfixed in practice. As online learning always performs on the sensitive data, we introduce the notion of differential privacy (DP) into our distributed online learning algorithm (DOLA) to protect the data privacy during the learning, which prevents an adversary from inferring any significant sensitive information. Our model is of general value for big data analytics in the distributed setting, because it can provide rigorous and scalable privacy proof and have much less computational complexity when compared to classic schemes, e.g., secure multiparty computation (SMC). To tackle high-dimensional incoming data entries, we study a sparse version of the DOLA with novel DP techniques to save the computing resources and improve the utility. Furthermore, we present two modified private DOLAs to meet the need of practical applications. One is to convert the DOLA to distributed stochastic optimization in an offline setting, the other is to use the mini-batches approach to reduce the amount of the perturbation noise and improve the utility. We conduct experiments on real datasets in a configured distributed platform. Numerical experiment results validate the feasibility of our private DOLAs.
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