Communication Compression for Distributed Nonconvex Optimization

This paper considers distributed nonconvex optimization with the cost functions being over agents. Noting that information compression is a key tool to reduce heavy communication load for algorithms as agents iteratively communicate neighbors, we propose three primal–dual compressed communication. The first two are applicable general class of compressors bounded relative error and third algorithm suitable classes absolute error. We show proposed have comparable convergence properties state-of-the-art exact Specifically, they can find first-order stationary points sublinear rate $\mathcal {O}(1/T)$ when each local function smooth, where notation="LaTeX">$T$ total number iterations, global optima linear under an additional condition satisfies Polyak–Łojasiewicz condition. Numerical simulations provided illustrate effectiveness theoretical results.