  The interactive recommender systems involve users in the recommendation
procedure by receiving timely user feedback to update the recommendation
policy. Therefore, they are widely used in real application scenarios. Previous
interactive recommendation methods primarily focus on learning users'
personalized preferences on the relevance properties of an item set. However,
the investigation of users' personalized preferences on the diversity
properties of an item set is usually ignored. To overcome this problem, we
propose the Linear Modular Dispersion Bandit (LMDB) framework, which is an
online learning setting for optimizing a combination of modular functions and
dispersion functions. Specifically, LMDB employs modular functions to model the
relevance properties of each item, and dispersion functions to describe the
diversity properties of an item set. Moreover, we also develop a learning
algorithm, called Linear Modular Dispersion Hybrid (LMDH) to solve the LMDB
problem and derive a gap-free bound on its n-step regret. Extensive experiments
on real datasets are performed to demonstrate the effectiveness of the proposed
LMDB framework in balancing the recommendation accuracy and diversity.
