Privacy-Preserving Diffusion Adaptive Learning With Nonzero-Mean Protection Noise

In this article, we consider the data privacy issue of distributed learning over adaptive networks under zero-mean protection noise. First, using a nonzero-mean protection noise, a new privacy-preserving diffusion adaptive least-mean-squares algorithm is devised, named NZPD-LMS. Different from the existing differential privacy noise, the nonzero-mean protection noise is designed with two noises with zero-mean and nonzero-mean, allowing the zero-mean noise to retain differential privacy properties, and the nonzero-mean noise to prevent the use of a sliding average over time to obtain transmission values. Then, based on mean-square analysis, we evaluate stability conditions and steady-state error bounds for the NZPD-LMS algorithm, as well as how each algorithmic parameter affects steady-state error. Finally, several simulations are conducted to illustrate the theoretical findings and effectiveness of the proposed approach.