A distributed optimization method with unknown cost function in a multi-agent system via randomized gradient-free method
Yipeng Pang, Guoqiang Hu · 2017
This paper presents a randomized gradient-free distributed optimization algorithm to solve the multi-agent optimization problem under a directed communication network. This algorithm builds random gradient-free oracles locally such that it can be utilized as a stochastic gradient information in each update. Different from most works on distributed optimization, this algorithm requires no explicit expressions but only local measurements of the cost function. We establish the convergence of this algorithm to a neighborhood of the optimal solution with the error bounded by some constant which depends on the selection of smoothing parameters and step-size. We demonstrate the effectiveness of this algorithm through numerical simulations.