A Distributed Optimization Method with Unknown Cost Function in Multi-Agent Systems via a Learning-Based Method
Yipeng Pang, Guoqiang Hu · 2019
This paper presents a distributed optimization algorithm to solve the unconstrained (not necessarily convex) optimization problems in a multi-agent system. The algorithm does not require any explicit expressions on the local cost functions, which means gradient information is not available. The only required information is the local measurements of the local cost function from each agent. The idea of the algorithm is to search for a better optimal point until no better points can be found. Each step-update is based on an estimation of the distance between the possible better points from the current point. The estimation is generated from a learning model, which is trained by the historical data of the step-updates. This algorithm does not require any assumptions on the convexity and differentiability of the local and/or global functions except that the solution exists and is finite. Convergence property of the proposed algorithm is carefully studied. Based on the idea of exploitation and exploration, it is shown that the algorithm is able to escape from the local optimum to find the best known optimum. A numerical example is provided to verify the performance of the proposed algorithm.