Causal Influence Maximization with Steady-State Guarantees

Abstract: 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.