Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions.

We consider the standard model of distributed optimization of a sum of functions , where node in a network holds the function (). We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node is capable of generating gradients of its function () corrupted by zero-mean bounded-support additive noise at each step, (ii) () is strongly convex, and (iii) each () has Lipschitz gradients.