  A general framework of personalized federated multi-armed bandits (PF-MAB) is
proposed, which is a new bandit paradigm analogous to the federated learning
(FL) framework in supervised learning and enjoys the features of FL with
personalization. Under the PF-MAB framework, a mixed bandit learning problem
that flexibly balances generalization and personalization is studied. A lower
bound analysis for the mixed model is presented. We then propose the
Personalized Federated Upper Confidence Bound (PF-UCB) algorithm, where the
exploration length is chosen carefully to achieve the desired balance of
learning the local model and supplying global information for the mixed
learning objective. Theoretical analysis proves that PF-UCB achieves an
$O(\log(T))$ regret regardless of the degree of personalization, and has a
similar instance dependency as the lower bound. Experiments using both
synthetic and real-world datasets corroborate the theoretical analysis and
demonstrate the effectiveness of the proposed algorithm.
