Personalised federated learning (FL) aims at collaboratively learning a machine learning model taylored for each client. Albeit promising advances have been made in this direction, most of existing approaches works do not allow for uncertainty quantification which is crucial in many applications. In addition, personalisation in the cross-device setting still involves important issues, especially for new clients or those having small number of observations. This paper aims at filling these gaps. To this end, we propose a novel methodology coined FedPop by recasting personalised FL into the population modeling paradigm where clients' models involve fixed common population parameters and random effects, aiming at explaining data heterogeneity. To derive convergence guarantees for our scheme, we introduce a new class of federated stochastic optimisation algorithms which relies on Markov chain Monte Carlo methods. Compared to existing personalised FL methods, the proposed methodology has important benefits: it is robust to client drift, practical for inference on new clients, and above all, enables uncertainty quantification under mild computational and memory overheads. We provide non-asymptotic convergence guarantees for the proposed algorithms and illustrate their performances on various personalised federated learning tasks.

翻译：个性化联邦学习旨在协同学习为每位客户端量身定制的机器学习模型。尽管该方向已取得可喜进展，但现有方法大多缺乏对诸多应用至关重要的不确定性量化能力。此外，跨设备场景下的个性化仍面临重大挑战，尤其是对于新客户端或观测数据量较少的客户端。本文致力于填补这些空白。为此，我们提出了一种名为FedPop的新方法，通过将个性化联邦学习重塑为群体建模范式，使客户端模型包含固定的共同群体参数和随机效应，旨在解释数据异质性。为推导该方案的收敛性保证，我们引入了一类基于马尔可夫链蒙特卡洛方法的新型联邦随机优化算法。与现有个性化联邦学习方法相比，所提方法具有重要优势：对客户端漂移具有鲁棒性，适用于新客户端的推理，更重要的是能在较低的计算和内存开销下实现不确定性量化。我们为所提算法提供了非渐进收敛性保证，并在多个个性化联邦学习任务上验证了其性能。