# Efficient Learning of Optimal Individualized Treatment Rules for Heteroscedastic or Misspecified Treatment-Free Effect Models

arXiv: https://arxiv.org/abs/2109.02570 · HTML: https://mlsanity.com/paper/2109.02570/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 71 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [Causal Inference: A Missing Data Perspective](https://mlsanity.com/paper/1712.06170/) (2017)
- [Efficient augmentation and relaxation learning for individualized treatment rules using observational data](https://mlsanity.com/paper/1901.00663/) (2019)
- [Multicategory Angle-based Learning for Estimating Optimal Dynamic Treatment Regimes with Censored Data](https://mlsanity.com/paper/2001.04629/) (2020)
- [Robust Q-learning](https://mlsanity.com/paper/2003.12427/) (2020)
- [Estimating Individualized Treatment Rules for Ordinal Treatments](https://mlsanity.com/paper/1702.04755/) (2017)
- [A Semiparametric Approach to Model Effect Modification](https://mlsanity.com/paper/1804.05373/) (2018)
- [Robust regression for optimal individualized treatment rules](https://mlsanity.com/paper/1604.03648/) (2016)
- [Near-optimal Individualized Treatment Recommendations](https://mlsanity.com/paper/2004.02772/) (2020)
- [Doubly Robust Direct Learning for Estimating Conditional Average Treatment Effect](https://mlsanity.com/paper/2004.10108/) (2020)

## Built on by (most cited first, 2 of 2)

- [PASTA: Pessimistic Assortment Optimization](https://mlsanity.com/paper/2302.03821/) (2023)
- [Neyman Meets Causal Machine Learning: Experimental Evaluation of Individualized Treatment Rules](https://mlsanity.com/paper/2404.17019/) (2024)

## Abstract (arXiv)

Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment-free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estimate can be consistent but may suffer from downgraded efficiency. Other than potential misspecified nuisance models, most existing methods do not account for the potential problem when the variance of outcome is heterogeneous among covariates and treatment. We observe that such heteroscedasticity can greatly affect the estimation efficiency of the optimal ITR. In this paper, we demonstrate that the consequences of misspecified treatment-free effect and heteroscedasticity can be unified as a covariate-treatment dependent variance of residuals. To improve efficiency of the estimated ITR, we propose an Efficient Learning (E-Learning) framework for finding an optimal ITR in the multi-armed treatment setting. We show that the proposed E-Learning is optimal among a regular class of semiparametric estimates that can allow treatment-free effect misspecification. In our simulation study, E-Learning demonstrates its effectiveness if one of or both misspecified treatment-free effect and heteroscedasticity exist. Our analysis of a Type 2 Diabetes Mellitus (T2DM) observational study also suggests the improved efficiency of E-Learning.