Set-Valued Policy Learning
Abstract
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.
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BibTeX
@misc{fuentesvicente2026setvalued,
title = {{Set-Valued Policy Learning}},
author = {Laura Fuentes-Vicente and Mathieu Even and Gaëlle Dormion and Antoine Chambaz and Uri Shalit and Julie Josse},
howpublished = {HAL},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.19830},
eprint = {2605.19830},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05673977v2},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Set-Valued Policy Learning
AU - Laura Fuentes-Vicente
AU - Mathieu Even
AU - Gaëlle Dormion
AU - Antoine Chambaz
AU - Uri Shalit
AU - Julie Josse
PY - 2026
DA - 2026/05/19
PB - HAL
DO - 10.48550/arxiv.2605.19830
UR - https://hal.science/hal-05673977v2
AB - 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.
ER -