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.