In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and heterogeneous data distributions. Two notable trends to deal with the communication overhead of federated algorithms are \emph{gradient compression} and \emph{local computation with periodic communication}. Despite many attempts, characterizing the relationship between these two approaches has proven elusive. We address this by proposing a set of algorithms with periodical compressed (quantized or sparsified) communication and analyze their convergence properties in both homogeneous and heterogeneous local data distributions settings. For the homogeneous setting, our analysis improves existing bounds by providing tighter convergence rates for both \emph{strongly convex} and \emph{non-convex} objective functions. To mitigate data heterogeneity, we introduce a \emph{local gradient tracking} scheme and obtain sharp convergence rates that match the best-known communication complexities without compression for convex, strongly convex, and nonconvex settings. We complement our theoretical results and demonstrate the effectiveness of our proposed methods by several experiments on real-world datasets.

通过定期压缩通信的算法，分析其收敛性并探讨其与局部计算的关系，提出了一种本地梯度追踪方案，以缓解数据异质性，实现了更快的收敛速度和更好的算法效果。

压缩联邦学习：统一分析和精确保证