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We consider the standard model of distributed optimization of a sum offunctions $F(\bz) = \sum_{i=1}^n f_i(\bz)$, where node $i$ in a network holdsthe function $f_i(\bz)$. We allow for a harsh network model characterized byasynchronous updates, message delays, unpredictable message losses, anddirected communication among nodes. In this setting, we analyze a modificationof the Gradient-Push method for distributed optimization, assuming that\begin{enumerate*}[label=(\roman*)] \item node $i$ is capable of generatinggradients of its function $f_i(\bz)$ corrupted by zero-mean bounded-supportadditive noise at each step, \item $F(\bz)$ is strongly convex, and \item each$f_i(\bz)$ has Lipschitz gradients. We show that our proposed methodasymptotically performs as well as the best bounds on centralized gradientdescent that takes steps in the direction of the sum of the noisy gradients ofall the functions $f_1(\bz), \ldots, f_n(\bz)$ at each step.

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