1Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs

Abstract—We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a dis-tributed way without requiring knowledge of either the number of agents or the graph sequence; each node is only required to know its out-degree at each time. Our main result is a convergence rate of O ((ln t)/t) for strongly convex functions with Lipschitz gradients even if only stochastic gradient samples are available; this is asymptotically faster than the O (ln t)