  Emerging mobility systems are increasingly capable of recommending options to
mobility users, to guide them towards personalized yet sustainable system
outcomes. Even more so than the typical recommendation system, it is crucial to
minimize regret, because 1) the mobility options directly affect the lives of
the users, and 2) the system sustainability relies on sufficient user
participation. In this study, we consider accelerating user preference learning
by exploiting a low-dimensional latent space that captures the mobility
preferences of users. We introduce a hierarchical contextual bandit framework
named Expert with Clustering (EWC), which integrates clustering techniques and
prediction with expert advice. EWC efficiently utilizes hierarchical user
information and incorporates a novel Loss-guided Distance metric. This metric
is instrumental in generating more representative cluster centroids. In a
recommendation scenario with $N$ users, $T$ rounds per user, and $K$ options,
our algorithm achieves a regret bound of $O(N\sqrt{T\log K} + NT)$. This bound
consists of two parts: the first term is the regret from the Hedge algorithm,
and the second term depends on the average loss from clustering. To the best of
the authors knowledge, this is the first work to analyze the regret of an
integrated expert algorithm with k-Means clustering. This regret bound
underscores the theoretical and experimental efficacy of EWC, particularly in
scenarios that demand rapid learning and adaptation. Experimental results
highlight that EWC can substantially reduce regret by 27.57% compared to the
LinUCB baseline. Our work offers a data-efficient approach to capturing both
individual and collective behaviors, making it highly applicable to contexts
with hierarchical structures. We expect the algorithm to be applicable to other
settings with layered nuances of user preferences and information.
