# A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity

arXiv: https://arxiv.org/abs/1911.09260 · HTML: https://mlsanity.com/paper/1911.09260/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 22 of 22)

- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [An Instrumental Variable Approach to Confounded Off-Policy Evaluation](https://mlsanity.com/paper/2212.14468/) (2022)
- [Estimating individual treatment effects under unobserved confounding using binary instruments](https://mlsanity.com/paper/2208.08544/) (2022)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [Safe Policy Learning through Extrapolation: Application to Pre-trial Risk Assessment](https://mlsanity.com/paper/2109.11679/) (2021)
- [Policy Learning with Asymmetric Counterfactual Utilities](https://mlsanity.com/paper/2206.10479/) (2022)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)
- [Conditional Instrumental Variable Regression with Representation Learning for Causal Inference](https://mlsanity.com/paper/2310.01865/) (2023)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Efficient and robust transfer learning of optimal individualized treatment regimes with right-censored survival data](https://mlsanity.com/paper/2301.05491/) (2023)
- [Policy Learning with Distributional Welfare](https://mlsanity.com/paper/2311.15878/) (2023)
- [Learning with Selectively Labeled Data from Multiple Decision-makers](https://mlsanity.com/paper/2306.07566/) (2023)
- [Reinforcement Learning with Continuous Actions Under Unmeasured Confounding](https://mlsanity.com/paper/2505.00304/) (2025)
- [Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning](https://mlsanity.com/paper/2302.12670/) (2023)
- [Statistical Estimation of Confounded Linear MDPs: An Instrumental Variable Approach](https://mlsanity.com/paper/2209.05186/) (2022)
- [Meta-analysis of individualized treatment rules via sign-coherency](https://mlsanity.com/paper/2211.15476/) (2022)
- [A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning](https://mlsanity.com/paper/2310.09545/) (2023)
- [Individualized Multi-Treatment Response Curves Estimation using RBF-net with Shared Neurons](https://mlsanity.com/paper/2401.16571/) (2024)
- [Deep Causal Behavioral Policy Learning: Applications to Healthcare](https://mlsanity.com/paper/2503.03724/) (2025)
- [Simulation-Based Sensitivity Analysis in Optimal Treatment Regimes and Causal Decomposition with Individualized Interventions](https://mlsanity.com/paper/2506.19010/) (2025)
- [Vector Search As Nearest Neighbor Matching: RAG-based Policy Learning in Causal Inference](https://mlsanity.com/paper/2607.18225/) (2026)

## Abstract (arXiv)

There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function E[YD(L)] for a given regime D and optimal regimes argmaxD E[YD(L)] with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a standard monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.