# Policy Learning under Biased Sample Selection

arXiv: https://arxiv.org/abs/2304.11735 · HTML: https://mlsanity.com/paper/2304.11735/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2023.

## Built on by (most cited first, 9 of 9)

- [Minimax Regret Learning for Data with Heterogeneous Subgroups](https://mlsanity.com/paper/2405.01709/) (2024)
- [Positivity-free Policy Learning with Observational Data](https://mlsanity.com/paper/2310.06969/) (2023)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Confounding-Robust Policy Improvement with Human-AI Teams](https://mlsanity.com/paper/2310.08824/) (2023)
- [Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference](https://mlsanity.com/paper/2606.00320/) (2026)
- [Taking a Moment for Distributional Robustness](https://mlsanity.com/paper/2405.05461/) (2024)
- [Sample size planning for conditional counterfactual mean estimation with a K-armed randomized experiment](https://mlsanity.com/paper/2403.04039/) (2024)
- [Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms](https://mlsanity.com/paper/2508.02812/) (2025)
- [Data Fusion for High-Resolution Estimation](https://mlsanity.com/paper/2508.14858/) (2025)

## Abstract (arXiv)

Practitioners often use data from a randomized controlled trial to learn a treatment assignment policy that can be deployed on a target population. A recurring concern in doing so is that, even if the randomized trial was well-executed (i.e., internal validity holds), the study participants may not represent a random sample of the target population (i.e., external validity fails)--and this may lead to policies that perform suboptimally on the target population. We consider a model where observable attributes can impact sample selection probabilities arbitrarily but the effect of unobservable attributes is bounded by a constant, and we aim to learn policies with the best possible performance guarantees that hold under any sampling bias of this type. In particular, we derive the partial identification result for the worst-case welfare in the presence of sampling bias and show that the optimal max-min, max-min gain, and minimax regret policies depend on both the conditional average treatment effect (CATE) and the conditional value-at-risk (CVaR) of potential outcomes given covariates. To avoid finite-sample inefficiencies of plug-in estimates, we further provide an end-to-end procedure for learning the optimal max-min and max-min gain policies that does not require the separate estimation of nuisance parameters.