Set-Valued Policy Learning
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913146394902528 |
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| author | Fuentes-Vicente, Laura Even, Mathieu Dormion, Gaëlle Chambaz, Antoine Shalit, Uri Josse, Julie |
| author_facet | Fuentes-Vicente, Laura Even, Mathieu Dormion, Gaëlle Chambaz, Antoine Shalit, Uri Josse, Julie |
| contents | Conventional treatment policies map patient covariates to a single recommended intervention in order to maximize expected clinical outcomes. Although a rich body of causal inference methods has been developed to estimate such policies, point-valued recommendations can be highly sensitive to estimation uncertainty, model specification, and finite-sample variability, while typically providing little guidance about how confident one should be in the recommended action. In this work, we propose a set-valued policy learning paradigm for the multiple-treatment setting, in which policies output a set of plausible treatments rather than a single recommendation. This formulation enables intrinsic uncertainty quantification, with the size of the predicted set reflecting the degree of decision ambiguity. We extend the learning-to-defer framework to multiple treatments via a novel \textit{greatest Lower Bound} method, and introduce \textit{conformal policy learning}, which bridges the gap between unobserved ground-truth optimal treatments and estimated optimal treatment rules. Drawing on insights from the noisy-label literature, we develop a randomness-injection approach that guarantees marginal coverage without requiring assumptions on underlying black-box optimal treatment rules. Through experiments on synthetic data and a real-world application to 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Set-Valued Policy Learning Fuentes-Vicente, Laura Even, Mathieu Dormion, Gaëlle Chambaz, Antoine Shalit, Uri Josse, Julie Machine Learning Statistics Theory Conventional treatment policies map patient covariates to a single recommended intervention in order to maximize expected clinical outcomes. Although a rich body of causal inference methods has been developed to estimate such policies, point-valued recommendations can be highly sensitive to estimation uncertainty, model specification, and finite-sample variability, while typically providing little guidance about how confident one should be in the recommended action. In this work, we propose a set-valued policy learning paradigm for the multiple-treatment setting, in which policies output a set of plausible treatments rather than a single recommendation. This formulation enables intrinsic uncertainty quantification, with the size of the predicted set reflecting the degree of decision ambiguity. We extend the learning-to-defer framework to multiple treatments via a novel \textit{greatest Lower Bound} method, and introduce \textit{conformal policy learning}, which bridges the gap between unobserved ground-truth optimal treatments and estimated optimal treatment rules. Drawing on insights from the noisy-label literature, we develop a randomness-injection approach that guarantees marginal coverage without requiring assumptions on underlying black-box optimal treatment rules. Through experiments on synthetic data and a real-world application to 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. |
| title | Set-Valued Policy Learning |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2605.19830 |