Zeroth-Order Diffusion Adaptive Filter over Networks

Most existing diffusion-based estimation algorithms require the explicit expression of the cost function in order to evaluate the stochastic gradient. In this work, we first discuss the zeroth-order (ZO) gradient for diffusion strategies, and present the ZO-diffusion algorithm that is suitable for applications where the explicit expression of the cost function is unavailable. In addition, to improve the convergence rate of the ZO-diffusion algorithm, we introduce a time-averaging stochastic variance reduced gradient (TA-SVRG) strategy, which is a variant of SVRG algorithm and designed to address online learning problems, and propose a ZO-TA-SVRG diffusion algorithm. Then, we analyze the mean and mean-square stability of the proposed ZO-TA-SVRG diffusion algorithm. Finally, simulation results are provided that demonstrate the performance and effectiveness of the proposed algorithms.