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

Abstract: We introduce families of stochastic interventions for 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 and a user-specified target, yielding closed-form Boltzmann-Gibbs couplings. The induced marginals define modified stochastic policies that interpolate smoothly, via a single tilt parameter, from the organic law or from the target distribution toward a product-of-experts limit when all destination costs are strictly positive. One of these families recovers and extends incremental propensity score interventions, retaining identification without global positivity. For inference, we derive efficient influence functions under a nonparametric model for the expected outcomes after these policies and construct one-step estimators with uniform confidence bands. 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. This could help close the loop between observational evidence and resource-aware experimental design.