# Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach

arXiv: https://arxiv.org/abs/2002.02579 · HTML: https://mlsanity.com/paper/2002.02579/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 17 of 17)

- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [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)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Policy Learning with Distributional Welfare](https://mlsanity.com/paper/2311.15878/) (2023)
- [Bayesian Safe Policy Learning with Chance Constrained Optimization: Application to Military Security Assessment during the Vietnam War](https://mlsanity.com/paper/2307.08840/) (2023)
- [Learning with Selectively Labeled Data from Multiple Decision-makers](https://mlsanity.com/paper/2306.07566/) (2023)
- [Distributionally Robust Causal Inference with Observational Data](https://mlsanity.com/paper/2210.08326/) (2022)
- [Predictive Performance Comparison of Decision Policies Under Confounding](https://mlsanity.com/paper/2404.00848/) (2024)
- [Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning](https://mlsanity.com/paper/2302.12670/) (2023)
- [When is Test-Time Adaptation Identifiable From Unlabeled Evidence?](https://mlsanity.com/paper/2609.11235/) (2026)
- [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)
- [Deep Causal Behavioral Policy Learning: Applications to Healthcare](https://mlsanity.com/paper/2503.03724/) (2025)
- [Vector Search As Nearest Neighbor Matching: RAG-based Policy Learning in Causal Inference](https://mlsanity.com/paper/2607.18225/) (2026)

## Abstract (arXiv)

Individualized treatment rules (ITRs) are considered a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate the average treatment effect conditional on a subject's covariate information, which is often challenging in observational studies due to the universal concern of unmeasured confounding. Instrumental variables (IVs) are widely-used tools to infer the treatment effect when there is unmeasured confounding between the treatment and outcome. In this work, we propose a general framework of approaching the optimal ITR estimation problem when a valid IV is allowed to only partially identify the treatment effect. We introduce a novel notion of optimality called "IV-optimality". A treatment rule is said to be IV-optimal if it minimizes the maximum risk with respect to the putative IV and the set of IV identification assumptions. We derive a bound on the risk of an IV-optimal rule that illuminates when an IV-optimal rule has favorable generalization performance. We propose a classification-based statistical learning method that estimates such an IV-optimal rule, design computationally-efficient algorithms, and prove theoretical guarantees. We contrast our proposed method to the popular outcome weighted learning (OWL) approach via extensive simulations, and apply our method to study which mothers would benefit from traveling to deliver their premature babies at hospitals with high level neonatal intensive care units.