Time-Varying Distributed Optimization for A Class of Stochastic Multi-Agent Systems
Wan-ying Li, Nan-jing Huang
TL;DR
This work tackles time-varying distributed optimization for stochastic multi-agent systems by first designing a centralized protocol that achieves exponential ultimate bounds on the tracking error in the mean-square sense via stochastic Lyapunov analysis. It then develops a fixed-time-estimator-based distributed approach that enables consensus and tracking under directed graphs, yielding MS-GEUB performance for the agents relative to the time-varying optimum. The authors provide rigorous stability results under a set of convexity, Lipschitz, and Hessian-sum assumptions, and validate the theory with simulations on small and moderately sized networks. The proposed framework advances privacy-preserving, robust distributed optimization in stochastic environments and suggests practical extensions to nonconvex problems and communication-efficient schemes.
Abstract
Distributed optimization problems have received much attention due to their privacy preservation, parallel computation, less communication, and strong robustness. This paper presents and studies the time-varying distributed optimization problem for a class of stochastic multi-agent systems for the first time. For this, we initially propose a protocol in the centralized case that allows the tracking error of the agent with respect to the optimal trajectory to be exponentially ultimately bounded in a mean-square sense by stochastic Lyapunov theory. We then generalize this to the distributed case. Therein, the global variable can be accurately estimated in a fixed-time by our proposed estimator. Based on this estimator, we design a new distributed protocol, and the results demonstrate that the tracking error of all agents with respect to the optimal trajectory is exponentially ultimately bound in a mean-square sense by stochastic Lyapunov theory. Finally, simulation experiments are conducted to validate the findings.