Decentralized and asynchronous communications are two popular techniques to
speedup communication complexity of distributed machine learning, by
respectively removing the dependency over a central orchestrator and the need
for synchronization. Yet, combining these two techniques together still remains
a challenge. In this paper, we take a step in this direction and introduce
Asynchronous SGD on Graphs (AGRAF SGD) -- a general algorithmic framework that
covers asynchronous versions of many popular algorithms including SGD,
Decentralized SGD, Local SGD, FedBuff, thanks to its relaxed communication and
computation assumptions. We provide rates of convergence under much milder
assumptions than previous decentralized asynchronous works, while still
recovering or even improving over the best know results for all the algorithms
covered.

分布机器学习中的去中心化和异步通信是提高通信复杂性的两种流行技术，而将这两种技术结合起来仍然是一个挑战。本文引入了一种名为 AGRAF SGD 的异步 SGD 算法框架，它包括了许多流行算法的异步版本，如 SGD、去中心化 SGD、本地 SGD 和 FedBuff，通过放松通信和计算假设，我们提供了比以前的去中心化异步工作更温和的收敛性速度，同时仍然恢复或甚至改善了所有涵盖算法的最佳结果。