Differentially private distributed logistic regression with the objective function perturbation

Distributed learning is a very effective divide-and-conquer strategy for dealing with big data. As distributed learning algorithms become more and more mature, network security issues including the risk of privacy disclosure of personal sensitive data, have attracted high attention and vigilance. Differentially private is an important method that maximizes the accuracy of a data query while minimizing the chance of identifying its records when querying from the given data. The known differentially private distributed learning algorithms are based on variable perturbation, but the variable perturbation method may be non-convergence and the experimental results usually have large deviations. Therefore, in this paper, we consider differentially private distributed learning algorithm based on objective function perturbation. We first propose a new distributed logistic regression algorithm based on objective function perturbation (DLR-OFP). We prove that the proposed DLR-OFP satisfies differentially private, and obtain its fast convergence rate by introducing a new acceleration factor for the gradient descent method. The numerical experiments based on benchmark data show that the proposed DLR-OFP algorithm has fast convergence rate and better privacy protection ability.