Communication efficient quasi-Newton distributed optimization based on the Douglas-Rachford envelope

Abstract: We consider distributed optimization in the client-server setting. By use of Douglas-Rachford splitting to the dual of the sum problem, we design a BFGS method that requires minimal communication (sending/receiving one vector per round for each client). Our method is line search free and achieves superlinear convergence. Experiments are also used to demonstrate the merits in decreasing communication and computation costs.