Influence maximization in networks is a central problem in machine learning and causal inference, where an intervention on a subset of individuals triggers a diffusion process through the network. Existing approaches typically optimize short-horizon rewards or rely on strong parametric assumptions, offering limited guarantees for longrun causal outcomes. In this work, we address the problem of selecting a seed set to maximize the total steady-state potential outcome under budget constraints. Theoretically, we demonstrate that under a low-probability propagation assumption, the high-dimensional path-dependent dynamics can be compressed into a low-dimensional exposure mapping with a bounded second-order approximation error. Leveraging this structural reduction, we propose CIM, a two-stage framework that first learns shape-constrained exposureresponse functions from observational data and then optimizes the objective via a greedy strategy. Our approach bridges causal inference with network optimization, providing provable guarantees for both the estimation of outcome functions and the approximation ratio of the influence maximization.

翻译：网络中的影响力最大化是机器学习和因果推断的核心问题，其中对个体子集的干预会通过网络触发扩散过程。现有方法通常优化短期回报或依赖于强参数假设，对长期因果结果的保证有限。本文研究在预算约束下选择种子集以最大化总稳态潜在结果的问题。理论上，我们证明在低概率传播假设下，高维路径依赖动态可被压缩为低维暴露映射，且其二阶近似误差有界。利用这一结构简化，我们提出CIM——一个两阶段框架：首先从观测数据中学习形状受限的暴露-响应函数，随后通过贪心策略优化目标函数。该方法将因果推断与网络优化相结合，为结果函数的估计和影响力最大化的近似比提供了可证明的保证。