做分布式机器学习或联邦学习的开发者，这篇论文给出了误差反馈算法的理论极限，帮你理解通信压缩到底能省多少而不损失收敛性，值得细读。
该论文针对分布式学习中通信瓶颈问题，对两种主流误差反馈算法（EF和EF21）进行了紧致收敛性分析。通过识别最优步长选择和构建最优Lyapunov函数，作者证明了这些算法在任意数量智能体下的收敛保证，并恢复了单智能体场景下已知的最佳结果。这项研究为理解误差反馈机制在分布式优化中的性能提供了理论基础，有助于设计更高效的通信压缩策略。
A Tight Theory of Error Feedback Algorithms in Distributed Optimization
Communication costs are a major bottleneck in distributed learning and first-order optimization. A common approach to alleviate this issue is to compress the gradient information exchanged between agents. However, such compression typically degrades the convergence guarantees of gradient-based methods. Error feedback mechanisms provide a simple and computationally cheap remedy for this issue, but numerous variants have been proposed, and their relative performance remains poorly understood. This paper provides tight convergence analyses for two of the main error-feedback algorithms from the literature, the classic Error Feedback method (EF) and Error Feedback 21 (EF21), by identifying optimal step-size choices and constructing optimal Lyapunov functions tailored to each method. The results hold independently of the number of agents and recover the known best guarantees possible in the single-agent regime.