Distributed Optimization Method Based On Optimal Control
Ziyuan Guo, Yue Sun, Yeming Xu, Liping Zhang, Huanshui Zhang
TL;DR
The paper reframes distributed optimization as an optimal-control problem for multi-agent systems, deriving a Riccati-based controller via the Pontryagin maximum principle. It presents two distributed schemes, DOCMC with a central server and DOAOC that uses consensus to replace matrix inversions, both incorporating average-gradient information to achieve fast convergence without explicit Hessian inversions. The authors establish global superlinear convergence under standard smoothness and strong convexity assumptions, and discuss practical simplifications for common network topologies. This work provides a principled bridge between optimal-control theory and distributed optimization, with potential impact on privacy-preserving, scalable coordination in networked systems.
Abstract
In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing the original objective function of itself and updated size for the future time instant. Compared with the existing distributed optimization problem for optimizing a sum of convex objective functions corresponding to multiple agents, we present a distributed optimization algorithm for multi-agents system based on the results from the maximum principle. Moreover, the convergence and superlinear convergence rate are also analyzed stringently.