Distributed Zero-Order Algorithms for Nonconvex Multi-Agent Optimization

Distributed multi-agent optimization is the core of many applications in distributed learning, control, estimation, etc. Most existing algorithms assume knowledge of first-order information of the objective and have been analyzed for convex problems. However, there are situations where the objective is nonconvex, and one can only obtain zero-order information of the objective. In this paper we consider derivative-free distributed algorithms for nonconvex multi-agent optimization, based on recent progress in zero-order optimization. We develop two algorithms for different settings, provide their convergence rates and compare them with existing centralized zero-order algorithms and first-order distributed algorithms.