Single Point-Based Distributed Zeroth-Order Optimization with a Non-Convex Stochastic Objective Function

Zero-order (ZO) optimization is a powerful tool for dealing with realistic constraints. On the other hand, the gradient-tracking (GT) technique proved to be an efficient method for distributed optimization aiming to achieve consensus. However, it is a first-order (FO) method that requires knowledge of the gradient, which is not always possible in practice. In this work, we introduce a zero-order distributed optimization method based on a one-point estimate of the gradient tracking technique. We prove that this new technique converges with a single noisy function query at a time in the non-convex setting. We then establish a convergence rate of O(frac1√[3]K) after a number of iterations K, which competes with that of O(frac1√[4]K) of its centralized counterparts. Finally, a numerical example validates our theoretical results.