arXiv:2608.13616cs.ROcs.LG2026-08

用邻接矩阵特征向量替代费德勒向量,实现更高效的分布式通信网络控制。

Adjacency-Based Spectral Proxy Control of Mobile Communication Agents

  • 将费德勒梯度控制器分解为局部交互规则与图嵌入组件,简化分布式实现。
  • 在相同通信轮数下,新方法比经典方法更稳定,避免网络断联。
  • 适合资源受限的移动通信网络,尤其适用于实时分布式控制场景。

我们研究由不可控任务代理和可控通信代理组成的异构移动代理网络,目标是随任务代理移动在线重定位通信代理。由于吞吐量目标不适用于实时控制,通常采用代数连通性等谱图度量作为代理目标。然而,控制代数连通性依赖于拉普拉斯矩阵第二小特征值对应的特征向量(即费德勒向量),其分布式估计需要无限多轮通信才能收敛。本文揭示了该费德勒梯度控制器的结构分解,提出使用更易分布式估计的替代嵌入。以具体实例A-Fiedler为例,用邻接矩阵主特征向量替代费德勒向量,该向量常用于将节点嵌入潜在几何空间。此表示在局部通信约束下更自然地支持分布式实现。实验表明,在无通信约束时性能相当,而在分布式估计下更具鲁棒性;例如,在相同通信轮数下,费德勒梯度可能收敛至断开配置,而我们的方法保持性能。我们认为该工作为分布式网络控制提供了更简洁路径。

原文摘要 · Abstract (English)

We consider a heterogeneous mobile-agent network composed of uncontrolled task agents and controllable communication agents. The objective is to reposition communication agents online as task agents move. Since throughput-based objectives are generally unsuitable for real-time control, spectral graph metrics such as algebraic connectivity are commonly adopted as surrogate objectives. However, controlling algebraic connectivity relies on the eigenvector corresponding to the second-smallest eigenvalue of a graph's Laplacian matrix (i.e., the Fiedler vector), whose distributed estimation requires an unbounded number of communication rounds to converge. In this work, we identify a structural decomposition of this Fiedler-gradient controller into a local interaction rule and a graph embedding component, suggesting the use of alternative embeddings that are easier to estimate distributively than the Fiedler vector. As a particular instance, we propose A-Fiedler, which replaces the Fiedler embedding with the dominant eigenvector of the adjacency matrix, commonly used as a graph embedding of nodes into a latent geometry. This representation is more naturally suited for distributed implementation under local communication constraints. We evaluate A-Fiedler against the classical Fiedler-gradient controller. Results show comparable network performance in the absence of communication constraints and improved robustness under distributed estimation. For instance, under the same number of communication rounds, the Fielder-gradient may even converge to disconnected configurations whereas our proposition maintains performance. We believe our contribution provides a simpler path toward distributed network control.

网络控制谱图理论分布式算法移动代理

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