线性阈值模型中的干预问题：一般化表述与新结果

中文摘要 AI 辅助

我们研究线性阈值模型的最优干预问题。这是一类流行的动态网络系统，其中许多智能体（与图的节点相对应）根据阈值规则策略性地改变其二元行动（0或1）。具体而言，当且仅当交互图中其邻居采取行动1的比例大于或等于规定阈值时，智能体才采取行动1。假设规划者可以以等于总阈值增加量的成本修改智能体的阈值，我们研究确保全局收敛到全1配置所需的最小干预成本。我们的主要贡献是引入一个新的图论量，称为有向路径数，即覆盖图所需的不相交路径的最小数量，这些路径可以被定向以形成有向无环图。当阈值都等于1/2时，最优成本被证明与有向路径数一致，而在一般情况下，它成为最优干预成本界限的主要组成部分。

英文摘要

We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

发表机构

• Politecnico di Torino（都灵理工大学）
• LISN, Université Paris Saclay（巴黎萨克雷大学 LISN 实验室）

机构由 AI 辅助整理，请以论文原文为准。