# Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding

arXiv: https://arxiv.org/abs/2105.01187 · HTML: https://mlsanity.com/paper/2105.01187/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 3 May 2021.

## Builds on (most cited first, 15 of 15)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables](https://mlsanity.com/paper/1611.09925/) (2016)
- [A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity](https://mlsanity.com/paper/1911.09260/) (2019)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Efficient augmentation and relaxation learning for individualized treatment rules using observational data](https://mlsanity.com/paper/1901.00663/) (2019)
- [High dimensional precision medicine from patient-derived xenografts](https://mlsanity.com/paper/1912.06667/) (2019)
- [Fast Optimal Bandwidth Selection for RBF Kernel using Reproducing Kernel Hilbert Space Operators for Kernel Based Classifiers](https://mlsanity.com/paper/1804.05214/) (2018)

## Built on by (most cited first, 21 of 21)

- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Optimizing Pessimism in Dynamic Treatment Regimes: A Bayesian Learning Approach](https://mlsanity.com/paper/2210.14420/) (2022)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Learning Complementary Policies for Human-AI Teams](https://mlsanity.com/paper/2302.02944/) (2023)
- [Unveiling and Causalizing CoT: A Causal Pespective](https://mlsanity.com/paper/2502.18239/) (2025)
- [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)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [Blessing from Human-AI Interaction: Super Reinforcement Learning in Confounded Environments](https://mlsanity.com/paper/2209.15448/) (2022)
- [RISE: Robust Individualized Decision Learning with Sensitive Variables](https://mlsanity.com/paper/2211.06569/) (2022)
- [Contextual Dynamic Pricing with Strategic Buyers](https://mlsanity.com/paper/2307.04055/) (2023)
- [Reinforcement Learning with Continuous Actions Under Unmeasured Confounding](https://mlsanity.com/paper/2505.00304/) (2025)
- [A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations](https://mlsanity.com/paper/2303.11187/) (2023)
- [Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning](https://mlsanity.com/paper/2302.12670/) (2023)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)
- [A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning](https://mlsanity.com/paper/2310.09545/) (2023)
- [Testing for Causal Fairness](https://mlsanity.com/paper/2502.12874/) (2025)
- [Decision-Aware Proximal Bridge Learning for Optimal Treatment Selection](https://mlsanity.com/paper/2605.16989/) (2026)
- [Proximal Mediation Analysis with Hidden Recanting Witnesses](https://mlsanity.com/paper/2606.17600/) (2026)

## Abstract (arXiv)

Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in observational studies. Motivated by the recent proposed proximal causal inference, we develop several proximal learning approaches to estimating optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. In particular, we establish several identification results for different classes of ITRs, exhibiting the trade-off between the risk of making untestable assumptions and the value function improvement in decision making. Based on these results, we propose several classification-based approaches to finding a variety of restricted in-class optimal ITRs and develop their theoretical properties. The appealing numerical performance of our proposed methods is demonstrated via an extensive simulation study and one real data application.