# Residual Weighted Learning for Estimating Individualized Treatment Rules

arXiv: https://arxiv.org/abs/1508.03179 · HTML: https://mlsanity.com/paper/1508.03179/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2015.

## Built on by (most cited first, 30 of 38)

- [Policy learning "without" overlap: Pessimism and generalized empirical Bernstein's inequality](https://mlsanity.com/paper/2212.09900/) (2022)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Policy Learning with Adaptively Collected Data](https://mlsanity.com/paper/2105.02344/) (2021)
- [Safe Exploration for Efficient Policy Evaluation and Comparison](https://mlsanity.com/paper/2202.13234/) (2022)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits](https://mlsanity.com/paper/2309.08748/) (2023)
- [Loss Functions for Discrete Contextual Pricing with Observational Data](https://mlsanity.com/paper/2111.09933/) (2021)
- [Reinforcement Learning in Modern Biostatistics: Constructing Optimal Adaptive Interventions](https://mlsanity.com/paper/2203.02605/) (2022)
- [Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression](https://mlsanity.com/paper/2207.09139/) (2022)
- [Bayesian Safe Policy Learning with Chance Constrained Optimization: Application to Military Security Assessment during the Vietnam War](https://mlsanity.com/paper/2307.08840/) (2023)
- [Reinforcement Learning for Individual Optimal Policy from Heterogeneous Data](https://mlsanity.com/paper/2505.09496/) (2025)
- [Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population](https://mlsanity.com/paper/2105.00581/) (2021)
- [Interpretable Off-Policy Learning via Hyperbox Search](https://mlsanity.com/paper/2203.02473/) (2022)
- [SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits](https://mlsanity.com/paper/2301.12357/) (2023)
- [A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning](https://mlsanity.com/paper/2307.13127/) (2023)
- [A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effect](https://mlsanity.com/paper/2310.06746/) (2023)
- [Efficient Learning of Optimal Individualized Treatment Rules for Heteroscedastic or Misspecified Treatment-Free Effect Models](https://mlsanity.com/paper/2109.02570/) (2021)
- [Prescriptive Machine Learning for Automated Decision Making: Challenges and Opportunities](https://mlsanity.com/paper/2112.08268/) (2021)
- [Stage-Aware Learning for Dynamic Treatments](https://mlsanity.com/paper/2310.19300/) (2023)
- [Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcome](https://mlsanity.com/paper/2104.10554/) (2021)
- [GEAR: On Optimal Decision Making with Auxiliary Data](https://mlsanity.com/paper/2104.10573/) (2021)
- [Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression](https://mlsanity.com/paper/2202.05245/) (2022)
- [BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect](https://mlsanity.com/paper/2211.10793/) (2022)
- [Counterfactual Learning with Multioutput Deep Kernels](https://mlsanity.com/paper/2211.11119/) (2022)
- [Optimal Policy Learning with Observational Data in Multi-Action Scenarios: Estimation, Risk Preference, and Potential Failures](https://mlsanity.com/paper/2403.20250/) (2024)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)
- [Off-Policy Evaluation Using Information Borrowing and Context-Based Switching](https://mlsanity.com/paper/2112.09865/) (2021)
- [Fusing Individualized Treatment Rules Using Secondary Outcomes](https://mlsanity.com/paper/2402.08828/) (2024)
- [Statistical Inference of Optimal Allocations I: Regularities and their Implications](https://mlsanity.com/paper/2403.18248/) (2024)
- [Neyman Meets Causal Machine Learning: Experimental Evaluation of Individualized Treatment Rules](https://mlsanity.com/paper/2404.17019/) (2024)

## Abstract (arXiv)

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. In this article, we propose a general framework, called Residual Weighted Learning (RWL), to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcomes, RWL weights these errors by residuals of the outcome from a regression fit on clinical covariates excluding treatment assignment. We utilize the smoothed ramp loss function in RWL, and provide a difference of convex (d.c.) algorithm to solve the corresponding non-convex optimization problem. By estimating residuals with linear models or generalized linear models, RWL can effectively deal with different types of outcomes, such as continuous, binary and count outcomes. We also propose variable selection methods for linear and nonlinear rules, respectively, to further improve the performance. We show that the resulting estimator of the treatment rule is consistent. We further obtain a rate of convergence for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed RWL methods is illustrated in simulation studies and in an analysis of cystic fibrosis clinical trial data.