Communication-Efficient Distributed SGD with Error-Feedback, Revisited
This work addresses a correctness issue in a communication-efficient distributed optimization method, which is incremental as it revises prior analysis without introducing new algorithmic improvements.
The paper identifies a mathematical flaw in the convergence proof of the dist-EF-SGD algorithm for distributed stochastic gradient descent, providing counter-examples to show the error bound is incorrect, and fixes it by deriving a new error bound and convergence theorem.
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. (NeurIPS 2019) 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 non-convex 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.