# Optimal Treatment Regimes for Proximal Causal Learning

arXiv: https://arxiv.org/abs/2212.09494 · HTML: https://mlsanity.com/paper/2212.09494/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 76 references that are in the map.
- First posted on arXiv 19 Dec 2022.

## Builds on (most cited first, 30 of 35)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [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)
- [Continuous State-Space Models for Optimal Sepsis Treatment - a Deep Reinforcement Learning Approach](https://mlsanity.com/paper/1705.08422/) (2017)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity](https://mlsanity.com/paper/1911.09260/) (2019)
- [Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference](https://mlsanity.com/paper/1908.11523/) (2019)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach](https://mlsanity.com/paper/2002.02579/) (2020)
- [A Selective Review of Negative Control Methods in Epidemiology](https://mlsanity.com/paper/2009.05641/) (2020)
- [Identifying effects of multiple treatments in the presence of unmeasured confounding](https://mlsanity.com/paper/2011.04504/) (2020)
- [Proximal Causal Inference for Complex Longitudinal Studies](https://mlsanity.com/paper/2109.07030/) (2021)
- [Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data](https://mlsanity.com/paper/1710.08074/) (2017)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021)
- [Efficient augmentation and relaxation learning for individualized treatment rules using observational data](https://mlsanity.com/paper/1901.00663/) (2019)
- [Selective machine learning of doubly robust functionals](https://mlsanity.com/paper/1911.02029/) (2019)
- [Optimal regimes for algorithm-assisted human decision-making](https://mlsanity.com/paper/2203.03020/) (2022)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)

## Built on by (most cited first, 5 of 5)

- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Policy Learning with Distributional Welfare](https://mlsanity.com/paper/2311.15878/) (2023)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)
- [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)

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.