Client-level fairness metrics for federated learning are used to ensure that all clients in a federation either: a) have similar final performance on their local data distributions (i.e., client parity), or b) obtain final performance on their local data distributions relative to their contribution to the federated learning process (i.e., contribution fairness). While a handful of works that propose either client-parity or contribution-based fairness metrics ground their definitions and decisions in social theories of equality -- such as distributive justice -- most works arbitrarily choose what notion of fairness to align with which makes it difficult for practitioners to choose which fairness metric aligns best with their fairness ethics. In this work, we propose UDJ-FL (Uncertainty-based Distributive Justice for Federated Learning), a flexible federated learning framework that can achieve multiple distributive justice-based client-level fairness metrics. Namely, by utilizing techniques inspired by fair resource allocation, in conjunction with performing aleatoric uncertainty-based client weighing, our UDJ-FL framework is able to achieve egalitarian, utilitarian, Rawls' difference principle, or desert-based client-level fairness. We empirically show the ability of UDJ-FL to achieve all four defined distributive justice-based client-level fairness metrics in addition to providing fairness equivalent to (or surpassing) other popular fair federated learning works. Further, we provide justification for why aleatoric uncertainty weighing is necessary to the construction of our UDJ-FL framework as well as derive theoretical guarantees for the generalization bounds of UDJ-FL. Our code is publicly available at https://github.com/alycia-noel/UDJ-FL.

本研究针对联邦学习中客户端公平性度量的选择问题，提出了一种名为UDJ-FL的灵活框架，实现多种基于分配公正的客户端公平性指标。研发中的技术既考虑了公平资源分配，也利用了基于不确定性的客户端加权，验证了UDJ-FL在实现公平性方面的有效性及其优越的泛化能力，这为实践者提供了更具指导意义的公平度量选择。 

通过不确定性量化实现联邦学习中的分配公正