Learning Optimal Distributionally Robust Individualized Treatment Rules

Abstract

Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. Many existing methods assume that the training and testing distributions are the same. However, the estimated optimal ITR may have poor generalizability when the training and testing distributions are not identical. In this article, we consider the problem of finding an optimal ITR from a restricted ITR class where there are some unknown covariate changes between the training and testing distributions. We propose a novel distributionally robust ITR (DR-ITR) framework that maximizes the worst-case value function across the values under a set of underlying distributions that are “close” to the training distribution. The resulting DR-ITR can guarantee the performance among all such distributions reasonably well. We further propose a calibrating procedure that tunes the DR-ITR adaptively to a small amount of calibration data from a target population. In this way, the calibrated DR-ITR can be shown to enjoy better generalizability than the standard ITR based on our numerical studies. Supplementary materials for this article are available online.

Keywords:

• Covariate shifts
• Distributionally robust optimization
• Generalizability
• Individualized treatment rules

This article is referred to by:

Discussion of Kallus (2020) and Mo, Qi, and Liu (2020): New Objectives for Policy Learning

Discussion of Kallus (2020) and Mo, Qi, and Liu (2020): New Objectives for Policy Learning

Supplementary Materials

The implementation details, technical proofs, and some additional numerical results are provided in the online supplementary materials.

Acknowledgments

The authors would like to thank the editor, the associate editor, and reviewers, whose helpful comments and suggestions led to a much improved presentation.

Additional information

Funding

The authors were supported in part by NSF grants IIS-1632951, DMS-1821231, and NIH grants R01GM126550 and P01 CA-142538.