A uniform momentum-based distributed stochastic gradient tracking algorithm for non-convex optimization - Li, Yantao; Wu, Chaoxu; Chen, Yingjue; Zhang, Keke; Lü, Qingguo; Deng, Shaojiang; Li, Huaqing (Journal of the Franklin Institute, 2025)
This paper investigates distributed non-convex optimization problems, specifically focusing on a collaborative approach to optimize a global non-convex objective function across agents over networks. Problems of this nature along with consideration of efficiency usually emerge in a number of applications in artificial intelligence and engineering, mostly evident in machine learning, resource management, etc. To this end, we propose a novel distributed stochastic momentum acceleration algorithm which providing a unified momentum acceleration paradigm for distributed stochastic gradient tracking methods. By adjusting the parameters of the proposed algorithm, different distributed momentum acceleration methods can be obtained. In theoretical analysis, we prove that the proposed algorithm is capable of converging to a neighbourhood of a first-order stationary point of the non-convex function with a sub-linear convergence rate. Moreover, the proposed algorithm is proved to achieve convergence independent of network topology under certain conditions. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed algorithm.