Gossip-based gradient-free method for multi-agent optimization: Constant step size analysis

In this paper we consider a distributed constrained convex optimization problem over a network composed of multiple interacting agents. For solving this problem, we propose a gossip-based gradient-free (GGF) method that only employs local computations and interactions between agents. For a constant step size, we study the convergence properties of the method, and more specifically, we derive some error bounds on the expected distance from the optimal value and the expected function value; we also highlight the dependence of the error bounds on the problem parameters.