Kernel-based Federated Learning with Personalization

We consider federated learning with personalization, where in addition to a global objective, each client is also interested in maximizing a personalized local objective. We consider this problem under a general continuous action space setting where the objective functions belong to a reproducing kernel Hilbert space. We propose algorithms based on surrogate Gaussian process (GP) models that achieve the optimal regret order (up to polylogarithmic factors). Furthermore, we show that the sparse approximations of the GP models significantly reduce the communication cost across clients.