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.

本文提出了一种在$\mathcal{X}$-臂赌博机框架下进行个性化联邦学习的新方法，旨在解决在高度异质环境中优化本地与全局目标的挑战。我们的方法通过结合个别客户偏好与聚合的全球知识的代理目标函数，灵活权衡个性化与集体学习。理论分析与实证评估表明，相较于现有方法，我们的方法表现出优越性，具有广泛的应用潜力。

具有灵活个性化的联邦$\mathcal{X}$-臂赌博机