Cost-Aware Interpolation of Soft Interventions: Blend of Propensity, Target Law, and Product of Experts

Johan de Aguas

Keywords: causal inference, stochastic interventions, policy design, semiparametric theory

Abstract: We introduce a family of stochastic interventions for discrete treatments that generalizes incremental propensity score interventions and bridges causal modeling with cost-sensitive domains. The formulation consists of a cost-penalized information projection problem of the independent product of the organic propensity and a user-specified target, yielding closed-form couplings. The induced marginals represent modified stochastic interventions and move smoothly, via a single tilt parameter, from the status quo or from the target distribution toward a product-of-experts limit when all destination costs are strictly positive. For inference, we derive efficient influence functions of their expected outcomes under a nonparametric model and construct one-step estimators with uniform confidence bands that exhibit stable performance and improved robustness relative to plug-in baselines. This framework can operationalizes graded scientific hypotheses under realistic constraints. Because the tilt is continuous, the costs and targets are modular, and expert-informed targets can integrate naturally with data-driven propensities, analysts can sweep feasible policy spaces, prototype candidates, and prioritize scarce experimental resources before committing them. This can help close the loop between observational evidence and resource-aware experimental design.

Submission Number: 15