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 <601 cGy to the bladder), with each plan evaluation being resource-intensive. 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. Critically, DMs must trust their final decision, confident they haven't missed superior alternatives; this trust is paramount in high-consequence scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates soft-hard bounds with probabilistic preference learning, maintaining distributions over DM preferences and bounds for adaptive Pareto subset refinement. This is guided by an active sampling strategy optimizing exploration-exploitation while minimizing cognitive burden. To build DM trust, Active-MoSH's global component, T-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 user study on AI-generated image selection further validates our hypotheses regarding the framework's ability to improve convergence, enhance DM trust, and provide expressive preference articulation, enabling more effective DMs.