  Conversational recommender systems have emerged as a potent solution for
efficiently eliciting user preferences. These systems interactively present
queries associated with "key terms" to users and leverage user feedback to
estimate user preferences more efficiently. Nonetheless, most existing
algorithms adopt a centralized approach. In this paper, we introduce FedConPE,
a phase elimination-based federated conversational bandit algorithm, where $M$
agents collaboratively solve a global contextual linear bandit problem with the
help of a central server while ensuring secure data management. To effectively
coordinate all the clients and aggregate their collected data, FedConPE uses an
adaptive approach to construct key terms that minimize uncertainty across all
dimensions in the feature space. Furthermore, compared with existing federated
linear bandit algorithms, FedConPE offers improved computational and
communication efficiency as well as enhanced privacy protections. Our
theoretical analysis shows that FedConPE is minimax near-optimal in terms of
cumulative regret. We also establish upper bounds for communication costs and
conversation frequency. Comprehensive evaluations demonstrate that FedConPE
outperforms existing conversational bandit algorithms while using fewer
conversations.
