Policy Learning under Unobserved Confounding: A Robust and Efficient Approach

TL;DR

This paper introduces a robust policy learning method that accounts for unobserved confounding using the marginal sensitivity model, enabling reliable decision-making from observational data even with potential hidden biases.

Contribution

It develops a novel framework combining MSM with distributionally robust optimization, providing closed-form welfare criteria and asymptotic guarantees for policies under unobserved confounding.

Findings

The method achieves robust policy performance in simulations.

It effectively handles unobserved confounding in empirical applications.

Provides theoretical regret bounds for the proposed policies.

Abstract

This paper develops a robust and efficient method for policy learning from observational data in the presence of unobserved confounding, complementing existing instrumental variable (IV) based approaches. We employ the marginal sensitivity model (MSM) to relax the commonly used yet restrictive unconfoundedness assumption by introducing a sensitivity parameter that captures the extent of selection bias induced by unobserved confounders. Building on this framework, we consider two distributionally robust welfare criteria, defined as the worst-case welfare and policy improvement functions, evaluated over an uncertainty set of counterfactual distributions characterized by the MSM. Closed-form expressions for both welfare criteria are derived. Leveraging these identification results, we construct doubly robust scores and estimate the robust policies by maximizing the proposed criteria. Our approach accommodates flexible machine learning methods for estimating nuisance components, even when these converge at moderately slow rate. We establish asymptotic regret bounds for the resulting policies, providing a robust guarantee against the most adversarial confounding scenario. The proposed method is evaluated through extensive simulation studies and empirical applications to the JTPA study and Head Start program.