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：本文通过一个多准则优化框架，定量校准联邦学习中全局模型与局部模型的性能，并将该框架转化为一个约束规划问题。每个设备的目标为其局部目标，在满足量化局部与全局模型接近程度的非线性约束条件下，设备力求最小化该目标。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始-对偶方法，称为“超越共识的联邦学习”（\texttt{FedBC}）。理论上，我们证明\texttt{FedBC}以匹配当前最优方法的速率收敛到一阶稳定点，但包含一个附加误差项，该误差项取决于为标量化多准则公式而引入的容差参数。最后，我们在多个数据集（Synthetic、MNIST、CIFAR-10、Shakespeare）上展示了\texttt{FedBC}能够平衡全局与局部模型的测试准确率指标，并取得了与当前最优方法相竞争的性能。