# Learning Optimal Distributionally Robust Individualized Treatment Rules Integrating Multi-Source Data

arXiv: https://arxiv.org/abs/2603.05568 · HTML: https://mlsanity.com/paper/2603.05568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Learning Optimal Distributionally Robust Individualized Treatment Rules](https://mlsanity.com/paper/2006.15121/) (2020)
- [Domain Adaptation Optimized for Robustness in Mixture Populations](https://mlsanity.com/paper/2407.20073/) (2024)
- [Estimating Unbounded Density Ratios: Applications in Error Control under Covariate Shift](https://mlsanity.com/paper/2504.01031/) (2025)
- [Policy Learning with Distributional Welfare](https://mlsanity.com/paper/2311.15878/) (2023)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)

## Abstract (arXiv)

Integrative analysis of multiple datasets for estimating optimal individualized treatment rules (ITRs) can enhance decision efficiency. A central challenge is posterior shift, wherein the conditional distribution of potential outcomes given covariates differs between source and target populations. We propose a prior information-based distributionally robust ITR (PDRO-ITR) that maximizes the worst-case policy value over a covariate-dependent distributional uncertainty set, ensuring robust performance under posterior shift. The uncertainty set is constructed as an individualized combination of source distributions, with weights combining prior source-membership probabilities and deviation terms constrained to the probability simplex to accommodate posterior shift. We derive a closed-form solution for the PDRO-ITR and develop an adaptive procedure to tune the uncertainty level. We establish risk bounds for the PDRO-ITR estimator, which guarantees robust performance under the worst case. Extensive simulations and two real-data applications demonstrate that the proposed method achieves superior performance compared to existing approaches.