A Hybrid Multi-Agent System Approach for Distributed Composite Convex Optimization Under Unbalanced Directed Graphs

IF 7.9 2区计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY IEEE Transactions on Network Science and Engineering Pub Date : 2025-01-17 DOI:10.1109/TNSE.2025.3527466

Zhu Wang;Dong Wang;Xiaopeng Xu;Jie Lian

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Abstract

This paper studies a distributed composite convex optimization problem for multi-agent systems over an unbalanced directed graph. The global objective function is the sum of local cost functions with known mathematical expressions and local cost functions with unknown ones. Due to the particularity of the local cost function, a hybrid multi-agent system composed of continuous-time dynamic agents and discrete-time dynamic agents is employed to solve such a problem. Also, because the local cost function may not be differentiable, a distributed algorithm based on subgradient and gradient-free oracle is proposed. Given some general assumptions, the developed algorithm almost surely converges to an approximately optimal solution. In addition, theoretical analysis indicates that the proposed algorithm possesses the same convergence rate as the existing stochastic gradient-free descent approaches under similar problem settings. Finally, a numerical example is provided to demonstrate the effectiveness of the findings.

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非平衡有向图下分布式复合凸优化的混合多代理系统方法

研究了非平衡有向图上多智能体系统的分布式复合凸优化问题。全局目标函数是数学表达式已知的局部代价函数和数学表达式未知的局部代价函数的和。由于局部代价函数的特殊性，采用由连续时间动态智能体和离散时间动态智能体组成的混合多智能体系统来解决这一问题。同时，针对局部代价函数不可微的情况，提出了一种基于次梯度和无梯度的分布式算法。给定一些一般的假设，所开发的算法几乎肯定收敛到一个近似最优解。此外，理论分析表明，在相似的问题设置下，该算法与现有的随机无梯度下降法具有相同的收敛速度。最后，通过数值算例验证了所得结果的有效性。

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来源期刊

IEEE Transactions on Network Science and Engineering Engineering-Control and Systems Engineering

CiteScore

12.60

自引率

9.10%

发文量

393

期刊介绍： The proposed journal, called the IEEE Transactions on Network Science and Engineering (TNSE), is committed to timely publishing of peer-reviewed technical articles that deal with the theory and applications of network science and the interconnections among the elements in a system that form a network. In particular, the IEEE Transactions on Network Science and Engineering publishes articles on understanding, prediction, and control of structures and behaviors of networks at the fundamental level. The types of networks covered include physical or engineered networks, information networks, biological networks, semantic networks, economic networks, social networks, and ecological networks. Aimed at discovering common principles that govern network structures, network functionalities and behaviors of networks, the journal seeks articles on understanding, prediction, and control of structures and behaviors of networks. Another trans-disciplinary focus of the IEEE Transactions on Network Science and Engineering is the interactions between and co-evolution of different genres of networks.