Communication-Efficient Distributed SGD with Error-Feedback, Revisited

We show that the convergence proof of a recent algorithm called dist-EF-SGD for distributed stochastic gradient descent with communication efficiency using error-feedback of Zheng et al., Communication-efficient distributed blockwise momentum SGD with error-feedback, in Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019 (NeurIPS 2019), 2019, pp. 11446–11456, is problematic mathematically. Concretely, the original error bound for arbitrary sequences of learning rate is unfortunately incorrect, leading to an invalidated upper bound in the convergence theorem for the algorithm. As evidences, we explicitly provide several counter-examples, for both convex and nonconvex cases, to show the incorrectness of the error bound. We fix the issue by providing a new error bound and its corresponding proof, leading to a new convergence theorem for the dist-EF-SGD algorithm, and therefore recovering its mathematical analysis.