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Motivated by distributed statistical learning over uncertain communicationnetworks, we study distributed stochastic optimization by networked nodes tocooperatively minimize a sum of convex cost functions. The network is modeledby a sequence of time-varying random digraphs with each node representing alocal optimizer and each edge representing a communication link. We considerthe distributed subgradient optimization algorithm with noisy measurements oflocal cost functions' subgradients, additive and multiplicative noises amonginformation exchanging between each pair of nodes. By stochastic Lyapunovmethod, convex analysis, algebraic graph theory and martingale convergencetheory, we prove that if the local subgradient functions grow linearly and thesequence of digraphs is conditionally balanced and uniformly conditionallyjointly connected, then proper algorithm step sizes can be designed so that allnodes' states converge to the global optimal solution almost surely.

Distributed Stochastic Optimization With Unbounded Subgradients Over Randomly Time-Varying Networks