Collaborative Learning in Kernel-based Bandits for Distributed Users

TL;DR

This paper introduces a collaborative kernel-based bandit learning algorithm for distributed clients, achieving order-optimal regret and reducing communication costs via sparse Gaussian process approximations.

Contribution

It proposes a novel collaborative learning algorithm using kernel methods with proven regret bounds and efficient communication strategies.

Findings

Achieves order-optimal regret performance.

Employs sparse GP models to reduce communication overhead.

Demonstrates effectiveness in distributed, personalized bandit settings.

Abstract

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.