随机图中的目标干预
Targeted Intervention in Random Graphs
摘要：
我们考虑一种设置，其中个人在网络中进行交互，每个人都选择作为邻居行为的函数来优化效用的行为。一个以均衡状态下社会福利最大化为目标的中央政府可以通过支付一定的成本来改变个体激励来进行干预，并且可以使用图的谱分解来计算最优干预，但是如果邻接矩阵未知，这在实践中是不可行的。在本文中，我们研究的问题，设计干预策略的邻接矩阵是未知的，并从一些分布图。对于几个常见的研究随机图模型，我们表明，有一个单一的干预，成比例的第一个特征向量的预期邻接矩阵，这是近最佳的几乎所有生成的图形时，预算是足够大的。我们还提供了几个有效的采样为基础的方法近似恢复的第一个特征向量时，我们不知道的分布。总的来说，我们的分析比较了三类干预措施：那些不使用网络数据的干预措施，那些使用一些数据（如分布知识或对图的查询）的干预措施，以及那些完全优化的干预措施。我们在合成和真实世界的网络数据上评估了这些干预策略，我们的研究结果表明，随机图模型的分析可以用于确定某些策略在实践中何时表现良好。
英文摘要：
We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying some cost to shift individual incentives, and the optimal intervention can be computed using the spectral decomposition of the graph, yet this is infeasible in practice if the adjacency matrix is unknown. In this paper, we study the question of designing intervention strategies for graphs where the adjacency matrix is unknown and is drawn from some distribution. For several commonly studied random graph models, we show that there is a single intervention, proportional to the first eigenvector of the expected adjacency matrix, which is near-optimal for almost all generated graphs when the budget is sufficiently large. We also provide several efficient sampling-based approaches for approximately recovering the first eigenvector when we do not know the distribution. On the whole, our analysis compares three categories of interventions: those which use no data about the network, those which use some data (such as distributional knowledge or queries to the graph), and those which are fully optimal. We evaluate these intervention strategies on synthetic and real-world network data, and our results suggest that analysis of random graph models can be useful for determining when certain heuristics may perform well in practice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
