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This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines compute gradients of a known empirical loss function using their own local data, and a master machine solves a related minimization problem to update the current estimate. We prove that for nonconvex nonsmooth problems, the proposed algorithm converges to a stationary point with a sublinear rate over the number of communication rounds, coinciding with the best theoretical rate that can be achieved for this class of problems. Linear convergence to a global minimum is established without any statistical assumptions on the local data for problems characterized by composite loss functions whose smooth part is strongly convex. Extensive numerical experiments verify that the performance of the proposed approach indeed improves - sometimes significantly - over other state-of-the-art algorithms in terms of total communication efficiency.

A Provably Communication-Efficient Asynchronous Distributed Inference Method for Convex and Nonconvex Problems