In many decision-making settings, the acceptability of new interventions depends on whether they do not reduce outcomes below a certain established threshold. For instance, in clinical medicine, new treatments are often only acceptable if they do not worsen outcomes relative to a standard of care. Safe Bayesian optimization aims to maximize an objective subject to safety constraints. In the context we consider, safety is defined relative to a known baseline policy whose outcomes are counterfactual and thus unobserved. Therefore, it is necessary to estimate the counterfactual outcomes of the baseline policy and use these (uncertain) estimates to safely optimize the objective. We address this estimation problem by employing conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we demonstrate how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. Additionally, we show how to adapt these conformal estimates to various types of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.
Blogger's Review: This paper presents a novel approach to handling safety in Bayesian optimization through counterfactual policies, which is particularly valuable in fields like medicine. By effectively estimating counterfactuals and using conformal predictions, it ensures the safety of the optimization process, providing new insights for future research. It's noteworthy to see how these theoretical methods can be practically implemented in real-world applications.