Federated learning (FL) was recently proposed to securely train models with data held over multiple locations ("clients") under the coordination of a central server. Two major challenges hindering the performance of FL algorithms are long training times caused by straggling clients and a decrease in training accuracy induced by non-iid local distributions ("client drift"). In this work we propose and analyze AREA, a new stochastic (sub)gradient algorithm that is robust to client drift and utilizes asynchronous communication to speed up convergence in the presence of stragglers. Moreover, AREA is, to the best of our knowledge, the first method that is both guaranteed to converge under arbitrarily long delays, and converges to an error neighborhood whose size depends only on the variance of the stochastic (sub)gradients used and thus is independent of both the heterogeneity between the local datasets and the length of client delays, without the use of delay-adaptive stepsizes. Our numerical results confirm our theoretical analysis and suggest that AREA outperforms state-of-the-art methods when local data are highly non-iid.

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