Over the past few years, the federated learning ($\texttt{FL}$) community has witnessed a proliferation of new $\texttt{FL}$ algorithms. However, our understating of the theory of $\texttt{FL}$ is still fragmented, and a thorough, formal comparison of these algorithms remains elusive. Motivated by this gap, we show that many of the existing $\texttt{FL}$ algorithms can be understood from an operator splitting point of view. This unification allows us to compare different algorithms with ease, to refine previous convergence results and to uncover new algorithmic variants. In particular, our analysis reveals the vital role played by the step size in $\texttt{FL}$ algorithms. The unification also leads to a streamlined and economic way to accelerate $\texttt{FL}$ algorithms, without incurring any communication overhead. We perform numerical experiments on both convex and nonconvex models to validate our findings.

翻译：过去几年，联邦学习（$\texttt{FL}$）领域涌现了大量新算法。然而，我们对联邦学习理论的理解仍较为零散，对这些算法进行全面、形式化的比较依然困难。受此现状启发，本文证明许多现有联邦学习算法可以从算子分裂的角度进行统一理解。这种统一框架使我们能够轻松比较不同算法、改进先前的收敛性结论并发现新的算法变体。特别地，我们的分析揭示了步长在联邦学习算法中发挥的关键作用。该统一框架还引发出一种精简且经济的联邦学习加速方案，且不会产生任何通信开销。我们在凸模型与非凸模型上进行了数值实验以验证相关结论。