Learning Optimal Distributionally Robust Individualized Treatment Rules

TL;DR

This paper introduces a distributionally robust approach to learning individualized treatment rules that remain effective under covariate distribution shifts between training and testing data, with adaptive calibration for improved generalizability.

Contribution

It proposes a novel distributionally robust ITR framework that maximizes worst-case outcomes and includes an adaptive calibration method for better real-world performance.

Findings

DR-ITR guarantees performance across similar distributions.

Calibration improves ITR generalizability with limited target data.

Numerical studies show superior performance over standard methods.

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 paper, we consider the problem of finding an optimal ITR from a restricted ITR class where there is 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.