Federated learning is a distributed machine learning paradigm, which aims to train a model using the local data of many distributed clients. A key challenge in federated learning is that the data samples across the clients may not be identically distributed. To address this challenge, personalized federated learning with the goal of tailoring the learned model to the data distribution of every individual client has been proposed. In this paper, we focus on this problem and propose a novel personalized Federated Learning scheme based on Optimal Transport (FedOT) as a learning algorithm that learns the optimal transport maps for transferring data points to a common distribution as well as the prediction model under the applied transport map. To formulate the FedOT problem, we extend the standard optimal transport task between two probability distributions to multi-marginal optimal transport problems with the goal of transporting samples from multiple distributions to a common probability domain. We then leverage the results on multi-marginal optimal transport problems to formulate FedOT as a min-max optimization problem and analyze its generalization and optimization properties. We discuss the results of several numerical experiments to evaluate the performance of FedOT under heterogeneous data distributions in federated learning problems.

翻译：联邦学习是一种分布式的机器学习模式,目的是用许多分布式客户的当地数据来培训一个模型。联邦学习的一个关键挑战是,客户的数据样本可能不会同样分布。为了应对这一挑战,提出了个性化联合会学习,目的是根据每个客户的数据分布量调整学习模式;在本文件中,我们着重这一问题,并提议一个基于最佳交通的新型个性化联邦学习计划,作为学习算法,学习将数据点传送到共同分布点的最佳运输图以及应用运输图下的预测模型。为了制定FEDOT问题,我们把标准的最佳运输任务从两种概率分布扩大到多边的最佳运输问题,目的是将样品从多种分布到共同概率领域运输。然后,我们利用多边际最佳运输问题的结果,将FEDOT作为一种微量优化问题,分析其一般化和优化特性。我们讨论了几个数字实验的结果,以评价FEDOT在联邦化数据分布过程中的复杂数据分布状况。学习问题。