Distributed Learning with Convex SUM-of -Non-Convex Objective

Recent research works have shown that some classical optimization methods originally designed for dealing with convex problems can demonstrate similar properties when applied to non-convex scenar-ios, where the problems are both locally and globally non-convex. This has led to the widespread development of distributed strategies for non-convex problems. When the sum of the local non-convex costs remains (strongly) convex and the individual local costs are smooth, it indicates a specific scenario that has notable applications and can benefit from existing solving methods. In this paper, drawing inspiration from the efficiency and stability of diffusion adaptation, we explore the minimization of a strongly convex sum of non-convex local costs. Specifically, we provide an analysis to demonstrate the convergence behavior of the network. Simulations are conducted to validate our theory.