In this work, we quantitatively calibrate the performance of global and local models in federated learning through a multi-criterion optimization-based framework, which we cast as a constrained program. The objective of a device is its local objective, which it seeks to minimize while satisfying nonlinear constraints that quantify the proximity between the local and the global model. By considering the Lagrangian relaxation of this problem, we develop a novel primal-dual method called Federated Learning Beyond Consensus (\texttt{FedBC}). Theoretically, we establish that \texttt{FedBC} converges to a first-order stationary point at rates that matches the state of the art, up to an additional error term that depends on a tolerance parameter introduced to scalarize the multi-criterion formulation. Finally, we demonstrate that \texttt{FedBC} balances the global and local model test accuracy metrics across a suite of datasets (Synthetic, MNIST, CIFAR-10, Shakespeare), achieving competitive performance with state-of-the-art.

翻译：本文通过一个基于多准则优化的框架，对联邦学习中全局模型与局部模型的性能进行定量校准，并将该框架表述为约束优化问题。每个设备的目标是其局部目标函数，在最小化该目标的同时需满足量化局部模型与全局模型接近程度的非线性约束。通过考虑该问题的拉格朗日松弛，我们提出了一种新颖的原-对偶方法——超越共识的联邦学习（FedBC）。理论分析表明，FedBC的收敛率与现有最优方法的一阶稳定点收敛率相当，仅额外增加一项依赖于容忍参数的误差项，该参数用于标量化多准则公式。最后，我们通过一系列数据集（Synthetic、MNIST、CIFAR-10、Shakespeare）验证了FedBC在平衡全局与局部模型测试准确率指标上的有效性，其性能与当前最优方法具有竞争力。