NPD-SG: A Noise-Resistant Primal-Dual Stochastic Gradient Diffusion Algorithm Over Networks

In this paper, we develop a noise-resistant primal-dual stochastic gradient-based diffusion algorithm (named NPD-SG) designed to operate effectively in scenarios with link noise. The mean-square analysis indicates that, with enough small step-size $\mu$ and forgetting factor $\gamma$ in (0, 1), the strategy is stable in terms of mean-square error; by reducing the value of $\gamma$, it is possible to maintain a low level of estimation error. Then, we modify the update step for dual variables to address the numerical accumulation problem, resulting in an improved NPD-SG (INPD-SG) algorithm. The theoretical analysis also reveals the impact of this modification on algorithm performance. Finally, several simulations demonstrate the theoretical findings and the effectiveness of the proposed approaches.