Interpolated stochastic interventions based on propensity scores, target policies and treatment-specific costs

TL;DR

This paper introduces a new class of stochastic interventions based on propensity scores and costs, enabling cost-sensitive decision making and robust causal inference without requiring global positivity.

Contribution

It develops a novel framework connecting causal modeling with cost-sensitive policies using cost-penalized information projections and Boltzmann-Gibbs couplings.

Findings

Proposed estimators outperform baseline methods in stability and robustness.

Framework allows flexible policy exploration under real-world constraints.

Extends incremental propensity score interventions to cost-sensitive contexts.

Abstract

We introduce two families of stochastic interventions with discrete treatments that connect causal modeling to cost-sensitive decision making. The interventions arise from a cost-penalized information projection of the independent product of the organic propensity scores and a reference policy, yielding closed-form Boltzmann-Gibbs couplings. The induced marginals define modified stochastic policies that interpolate smoothly, via a tilt parameter, from the organic law or from the reference law toward a product-of-experts limit when all destination costs are strictly positive. The first family recovers and extends incremental propensity score interventions, retaining identification without global positivity. For inference on the expected outcomes after these policies, we derive the efficient influence functions under a nonparametric model and construct one-step estimators. In simulations, the proposed estimators improve stability and robustness to nuisance misspecification relative to plug-in baselines. The framework can operationalize graded scientific hypotheses under realistic constraints. Because inputs are modular, analysts can sweep feasible policy spaces, prototype candidates, and align interventions with budgets and logistics before committing experimental resources.