Privacy-Preserving Dual Averaging With Arbitrary Initial Conditions for Distributed Optimization

This article considers a privacy-concerned distributed optimization problem over multiagent networks, in which malicious agents exist and try to infer the privacy information of the normal ones. We propose a novel dual averaging algorithm which involves the use of a correlated perturbation mechanism to preserve the privacy of the normal agents. It is shown that our algorithm achieves deterministic convergence under arbitrary initial conditions and the privacy preservation is guaranteed. Moreover, a probability density function of the perturbation is given to maximize the degree of privacy measured by the trace of the Fisher information matrix. Finally, a numerical example is provided to illustrate the effectiveness of our algorithm.

Automated summary

This article discusses a distributed optimization problem with privacy concerns in multi-agent networks where malicious agents try to infer the privacy information of normal agents. A novel dual averaging algorithm is proposed that utilizes a correlated perturbation mechanism to protect the privacy of normal agents. It is proven that the algorithm achieves deterministic convergence under any initial conditions while guaranteeing privacy preservation. Furthermore, a probability density function for the perturbation is provided to maximize privacy measured by the trace of the Fisher information matrix. Lastly, a numerical example is presented to illustrate the effectiveness of the algorithm.