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We study collaborative learning among distributed clients facilitated by acentral server. Each client is interested in maximizing a personalizedobjective function that is a weighted sum of its local objective and a globalobjective. Each client has direct access to random bandit feedback on its localobjective, but only has a partial view of the global objective and relies oninformation exchange with other clients for collaborative learning. We adoptthe kernel-based bandit framework where the objective functions belong to areproducing kernel Hilbert space. We propose an algorithm based on surrogateGaussian process (GP) models and establish its order-optimal regret performance(up to polylogarithmic factors). We also show that the sparse approximations ofthe GP models can be employed to reduce the communication overhead acrossclients.

Collaborative Learning in Kernel-based Bandits for Distributed Users