# Policy Learning with Distributional Welfare

arXiv: https://arxiv.org/abs/2311.15878 · HTML: https://mlsanity.com/paper/2311.15878/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 73 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity](https://mlsanity.com/paper/1911.09260/) (2019)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach](https://mlsanity.com/paper/2002.02579/) (2020)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Safe Policy Learning through Extrapolation: Application to Pre-trial Risk Assessment](https://mlsanity.com/paper/2109.11679/) (2021)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)
- [Median Optimal Treatment Regimes](https://mlsanity.com/paper/2103.01802/) (2021)
- [On Robustness of Individualized Decision Rules](https://mlsanity.com/paper/1903.04367/) (2019)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Comment: Individualized Treatment Rules Under Endogeneity](https://mlsanity.com/paper/2010.07656/) (2020)
- [Constrained Classification and Policy Learning](https://mlsanity.com/paper/2106.12886/) (2021)
- [Inference on Optimal Dynamic Policies via Softmax Approximation](https://mlsanity.com/paper/2303.04416/) (2023)
- [Assessing Heterogeneity of Treatment Effects](https://mlsanity.com/paper/2306.15048/) (2023)
- [Treatment Choice, Mean Square Regret and Partial Identification](https://mlsanity.com/paper/2310.06242/) (2023)

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

- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)
- [Preference-based Conditional Treatment Effects and Policy Learning](https://mlsanity.com/paper/2602.03823/) (2026)
- [Learning Optimal Distributionally Robust Individualized Treatment Rules Integrating Multi-Source Data](https://mlsanity.com/paper/2603.05568/) (2026)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)

## Abstract (arXiv)

In this paper, we explore optimal treatment allocation policies that target distributional welfare. Most literature on treatment choice has considered utilitarian welfare based on the conditional average treatment effect (ATE). While average welfare is intuitive, it may yield undesirable allocations especially when individuals are heterogeneous (e.g., with outliers) - the very reason individualized treatments were introduced in the first place. This observation motivates us to propose an optimal policy that allocates the treatment based on the conditional quantile of individual treatment effects (QoTE). Depending on the choice of the quantile probability, this criterion can accommodate a policymaker who is either prudent or negligent. The challenge of identifying the QoTE lies in its requirement for knowledge of the joint distribution of the counterfactual outcomes, which is not generally point-identified. We introduce minimax policies that are robust to this model uncertainty. A range of identifying assumptions can be used to yield more informative policies. For both stochastic and deterministic policies, we establish the asymptotic bound on the regret of implementing the proposed policies. The framework can be generalized to any setting where welfare is defined as a functional of the joint distribution of the potential outcomes.