Federated $\mathcal{X}$-armed Bandit with Flexible Personalisation

TL;DR

This paper presents a new federated learning method within the $\\mathcal{X}$-armed bandit framework that balances personalisation and global knowledge, achieving low regret and communication efficiency in heterogeneous environments.

Contribution

It introduces a surrogate objective and a phase-based elimination algorithm for flexible personalisation in federated bandits, with theoretical and empirical validation.

Findings

Achieves sublinear regret with logarithmic communication overhead.

Effective in highly heterogeneous environments.

Outperforms existing methods in empirical evaluations.

Abstract

This paper introduces a novel approach to personalised federated learning within the $\mathcal{X}$-armed bandit framework, addressing the challenge of optimising both local and global objectives in a highly heterogeneous environment. Our method employs a surrogate objective function that combines individual client preferences with aggregated global knowledge, allowing for a flexible trade-off between personalisation and collective learning. We propose a phase-based elimination algorithm that achieves sublinear regret with logarithmic communication overhead, making it well-suited for federated settings. Theoretical analysis and empirical evaluations demonstrate the effectiveness of our approach compared to existing methods. Potential applications of this work span various domains, including healthcare, smart home devices, and e-commerce, where balancing personalisation with global insights is crucial.