首次用连续时间分析联邦平均，揭示其收敛与泛化机制。
Continuous-Time Analysis of Federated Averaging
- 将联邦平均建模为多变量随机微分方程，从连续时间视角分析。
- 在多种损失函数下建立收敛性保证，覆盖更广的数据异质性场景。
- 发现服务器权重更新可近似为正态分布，适用于理论研究者。
联邦平均（FedAvg）是水平联邦学习中广泛应用的算法，客户端样本不共享给其他客户端或中心服务器。现有大量关于离散迭代设置下FedAvg的收敛性分析，涵盖多种损失函数和数据异质性水平。本文首次将其分析拓展至连续时间框架，其中全局权重遵循多变量随机微分方程（SDE）演化。利用随机过程技术，在不同损失函数下建立了收敛性保证，部分结果比现有离散设定更通用。同时，给出了FedAvg对服务器权重更新可近似为正态随机变量的条件。最后，基于连续时间形式揭示了FedAvg的泛化特性。
原文摘要 · Abstract (English)
Federated averaging (FedAvg) is a popular algorithm for horizontal federated learning (FL), where samples are gathered across different clients and are not shared with each other or a central server. Extensive convergence analysis of FedAvg exists for the discrete iteration setting, guaranteeing convergence for a range of loss functions and varying levels of data heterogeneity. We extend this analysis to the continuous-time setting where the global weights evolve according to a multivariate stochastic differential equation (SDE), which is the first time FedAvg has been studied from the continuous-time perspective. We use techniques from stochastic processes to establish convergence guarantees under different loss functions, some of which are more general than existing work in the discrete setting. We also provide conditions for which FedAvg updates to the server weights can be approximated as normal random variables. Finally, we use the continuous-time formulation to reveal generalization properties of FedAvg.
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