  We consider the distributed optimization problem for the sum of convex
functions where the underlying communications network connecting agents at each
time is drawn at random from a collection of directed graphs. Building on an
earlier work [15], where a modified version of the subgradient-push algorithm
is shown to be almost surely convergent to an optimizer on sequences of random
directed graphs, we find an upper bound of the order of $\sim
O(\frac{1}{\sqrt{t}})$ on the convergence rate of our proposed algorithm,
establishing the first convergence bound in such random settings.
