Distributionally Robust Policy Learning with Wasserstein Distance

TL;DR

This paper introduces a distributionally robust approach to policy learning that accounts for population differences using Wasserstein distance, providing a new estimator that improves treatment rule performance in target populations.

Contribution

It develops a novel Wasserstein-distance-based distributionally robust estimator for individualized treatment rules that performs well even with limited or source population data.

Findings

The proposed estimator outperforms naive methods in target population scenarios.

The approach offers simple intuition and estimation procedures.

Theoretical performance guarantees are provided.

Abstract

The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs assume that the available experimental or observational data are derived from the target population in which the estimated policy is implemented. However, this assumption often fails in practice because of limited useful data. In this case, policymakers must rely on the data generated in the source population, which differs from the target population. Unfortunately, existing estimation methods do not necessarily work as expected in the new setting, and strategies that can achieve a reasonable goal in such a situation are required. This study examines the application of distributionally robust optimization (DRO), which formalizes an ambiguity about the target population and adapts to the worst-case scenario in the set. It is shown that DRO with Wasserstein distance-based characterization of ambiguity provides simple intuitions and a simple estimation method. I then develop an estimator for the distributionally robust ITR and evaluate its theoretical performance. An empirical application shows that the proposed approach outperforms the naive approach in the target population.