A Scaling-Function Approach for Distributed Constrained Optimization in Unbalanced Multiagent Networks
A Scaling-Function Approach for Distributed Constrained Optimization in Unbalanced Multiagent Networks
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DOI：
10.1109/tac.2021.3131678
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发表时间：
2022-11
影响因子：
6.8
通讯作者：
Fei Chen;Jin Jin-Jin;Linying Xiang;W. Ren
中科院分区：
文献类型：
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作者：
Fei Chen;Jin Jin-Jin;Linying Xiang;W. Ren
针对凸约束下的非平衡多智能体网络的分布式优化问题，提出了一种基于标度函数的方法。该算法的特点是不需要利用智能体的出度信息，也不需要估计Laplacian矩阵的零特征值对应的左特征向量。现有的非平衡网络的方法要么需要知道代理的出度，这在应用中是不切实际的，其中一个代理可能不知道其他代理的检测和使用它的信息，或者要求每个代理配备一个网络大小的估计器，导致额外的存储和通信成本为$n^2$，$n$是网络大小。结果表现出的缩放因子的选择和算法的收敛性能之间的内在联系，在其他已知的因素，如网络拓扑结构和局部目标函数的次梯度的有界性。数值例子验证了理论结果。
This article aims at developing a scaling-function approach for distributed optimization of unbalanced multiagent networks under convex constraints. The distinguishing feature of the algorithm is that it does not employ agents’ out-degree information, nor does it require the estimation of the left eigenvector, corresponding to the zero eigenvalue, of the Laplacian matrix. Existing approaches for unbalanced networks either demand the knowledge on agents’ out-degrees, which is impractical in applications, where an agent might not be aware of the detection and employment of its information by other agents, or require every agent to be equipped with a network-sized estimator, causing an additional $n^2$ storage and communication cost with $n$ being the network size. The results exhibit an inherent connection between the selection of the scaling factor and the convergence property of the algorithm, among other known factors such as the network topology and the boundedness of the subgradients of the local objective functions. Numerical examples are provided to validate the theoretical findings.