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

2026-03-05

AI Summary

This study addresses the degradation in generalizability of individualized treatment rules (ITRs) caused by posterior shift—i.e., differences in the conditional distributions of potential outcomes across populations—in multi-source data integration. To tackle this challenge, we propose a prior information–driven distributionally robust ITR (PDRO-ITR) that constructs a covariate-dependent distributional uncertainty set by incorporating prior source probabilities and a bias term, and optimizes the policy value under the worst-case scenario. We derive a closed-form solution for the PDRO-ITR and develop an adaptive tuning mechanism to calibrate the uncertainty level. Theoretical analysis establishes a worst-case risk bound, and both simulation studies and analyses of two real-world datasets demonstrate that the proposed method consistently outperforms existing approaches in terms of robustness and performance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• individualized treatment rules
• posterior shift
• multi-source data
• distributional robustness
• conditional distribution

Innovation

• distributionally robust optimization
• individualized treatment rules
• posterior shift
• multi-source data integration
• uncertainty set