Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds

High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of >95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of <601cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-MoSH's global component, C-MoSH, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-MoSH's performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework's ability to improve convergence, enhance DM confidence, and provide expressive preference articulation.