  A critical factor in the success of decision support systems is the accurate
modeling of user preferences. Psychology research has demonstrated that users
often develop their preferences during the elicitation process, highlighting
the pivotal role of system-user interaction in developing personalized systems.
This paper introduces a novel approach, combining Large Language Models (LLMs)
with Constraint Programming to facilitate interactive decision support. We
study this hybrid framework through the lens of meeting scheduling, a
time-consuming daily activity faced by a multitude of information workers. We
conduct three studies to evaluate the novel framework, including a diary study
(n=64) to characterize contextual scheduling preferences, a quantitative
evaluation of the system's performance, and a user study (n=10) with a
prototype system. Our work highlights the potential for a hybrid LLM and
optimization approach for iterative preference elicitation and design
considerations for building systems that support human-system collaborative
decision-making processes.
