# Set-Valued Policy Learning

arXiv: https://arxiv.org/abs/2605.19830 · HTML: https://mlsanity.com/paper/2605.19830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 19 May 2026.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [CoinDICE: Off-Policy Confidence Interval Estimation](https://mlsanity.com/paper/2010.11652/) (2020)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Improving Expert Predictions with Conformal Prediction](https://mlsanity.com/paper/2201.12006/) (2022)
- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [On the Utility of Prediction Sets in Human-AI Teams](https://mlsanity.com/paper/2205.01411/) (2022)
- [Nonparametric causal effects based on incremental propensity score interventions](https://mlsanity.com/paper/1704.00211/) (2017)
- [Designing Decision Support Systems Using Counterfactual Prediction Sets](https://mlsanity.com/paper/2306.03928/) (2023)
- [Conformal Off-Policy Prediction in Contextual Bandits](https://mlsanity.com/paper/2206.04405/) (2022)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Towards Human-AI Complementarity with Prediction Sets](https://mlsanity.com/paper/2405.17544/) (2024)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [Label Noise Robustness of Conformal Prediction](https://mlsanity.com/paper/2209.14295/) (2022)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Experimental Evaluation of Algorithm-Assisted Human Decision-Making: Application to Pretrial Public Safety Assessment](https://mlsanity.com/paper/2012.02845/) (2020)
- [Conformal Off-policy Prediction](https://mlsanity.com/paper/2206.06711/) (2022)
- [Predictive Inference with Weak Supervision](https://mlsanity.com/paper/2201.08315/) (2022)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [Conformal prediction intervals for the individual treatment effect](https://mlsanity.com/paper/2006.01474/) (2020)
- [Treatment Allocation under Uncertain Costs](https://mlsanity.com/paper/2103.11066/) (2021)
- [Conformal Prediction and Human Decision Making](https://mlsanity.com/paper/2503.11709/) (2025)
- [How many labelers do you have? A closer look at gold-standard labels](https://mlsanity.com/paper/2206.12041/) (2022)
- [Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2402.04906/) (2024)

## Abstract (arXiv)

Conventional treatment policies map patient covariates to a single recommended intervention in order to maximize expected clinical outcomes. However, when multiple treatments yield statistically indistinguishable outcomes or when treatment has no effect, recommending a single intervention may result in somewhat arbitrary interventions, undermining clinical adoption and trust. To address this, we propose a set-valued policy learning paradigm. By outputting sets of valuable treatments whose cardinality reflects the recommendation's ambiguity, our approach better supports clinical decision-making. Evaluating a set-valued policy proves subtle due to the range of possible downstream decisions. To do so, we define the set-policy value using a choice function to model clinical decision-making, and we develop doubly robust estimators thereof. Despite its practical importance, set-valued policy learning for categorical treatments remains largely unexplored. In this context, we introduce two complementary approaches: the Greatest Lower Bound method, which extends the learning-to-defer framework to multiple treatments, and conformal set-valued policy learning, which bridges the gap between unobserved ground-truth optimal treatments and estimated optimal treatment rules. Through experiments on synthetic data and real-world applications to trauma care and in-vitro fertilization (IVF), we demonstrate that our methods produce robust and actionable policies that naturally incorporate clinical considerations while effectively balancing performance and reliability.