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.
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