# Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox

arXiv: https://arxiv.org/abs/2110.10961 · HTML: https://mlsanity.com/paper/2110.10961/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (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)
- [Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach](https://mlsanity.com/paper/2002.02579/) (2020)
- [On falsification of the binary instrumental variable model](https://mlsanity.com/paper/1605.03677/) (2016)
- [Comment: Individualized Treatment Rules Under Endogeneity](https://mlsanity.com/paper/2010.07656/) (2020)
- [Identification in Nonparametric Models for Dynamic Treatment Effects](https://mlsanity.com/paper/1805.09397/) (2018)
- [On a necessary and sufficient identification condition of optimal treatment regimes with an instrumental variable](https://mlsanity.com/paper/2010.03390/) (2020)

## Built on by (most cited first, 8 of 8)

- [Statistical Comparisons of Classifiers by Generalized Stochastic Dominance](https://mlsanity.com/paper/2209.01857/) (2022)
- [Policy Learning with Asymmetric Counterfactual Utilities](https://mlsanity.com/paper/2206.10479/) (2022)
- [Minimax Regret Learning for Data with Heterogeneous Subgroups](https://mlsanity.com/paper/2405.01709/) (2024)
- [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)
- [Distributionally Robust Causal Inference with Observational Data](https://mlsanity.com/paper/2210.08326/) (2022)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)
- [A Sensitivity Approach to Causal Inference Under Limited Overlap](https://mlsanity.com/paper/2511.22003/) (2025)

## Abstract (arXiv)

Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification in a comprehensive manner. We establish a formal link between individualized decision-making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision-making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.