Differentially Private Distributed Online Optimization via Signs of Relative States

In this paper, a privacy-preserving distributed online optimization algorithm is proposed. Specifically, the proposed algorithm achieves rigorous ?-differential privacy through the injection of Laplace noise, and each node updates its state using only the sign of the difference between its neighbors' states and its own, which enhances the robustness to noise. It is also proved that the proposed algorithm achieves an O(vT) expected regret, which is identical to the existing algorithms without considering privacy preservation. Moreover, the proposed algorithm relaxes the requirement for the connected network to have a stochastic weight adjacency matrix. Numerical experiments are provided to validate the effectiveness of the proposed algorithm.