Collaborative Learning in Kernel-based Bandits for Distributed Users
This addresses the problem of efficient distributed learning for users with mixed objectives, offering a method to reduce communication overhead, though it is incremental as it builds on existing kernel-based bandit frameworks.
The paper tackles collaborative learning among distributed clients with personalized objectives, combining local and global goals, and achieves order-optimal regret performance up to polylogarithmic factors using kernel-based bandits and surrogate Gaussian process models.
We study collaborative learning among distributed clients facilitated by a central server. Each client is interested in maximizing a personalized objective function that is a weighted sum of its local objective and a global objective. Each client has direct access to random bandit feedback on its local objective, but only has a partial view of the global objective and relies on information exchange with other clients for collaborative learning. We adopt the kernel-based bandit framework where the objective functions belong to a reproducing kernel Hilbert space. We propose an algorithm based on surrogate Gaussian process (GP) models and establish its order-optimal regret performance (up to polylogarithmic factors). We also show that the sparse approximations of the GP models can be employed to reduce the communication overhead across clients.