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We consider a distributed stochastic optimization problem in networks withfinite number of nodes. Each node adjusts its action to optimize the globalutility of the network, which is defined as the sum of local utilities of allnodes. Gradient descent method is a common technique to solve the optimizationproblem, while the computation of the gradient may require much informationexchange. In this paper, we consider that each node can only have a noisynumerical observation of its local utility, of which the closed-form expressionis not available. This assumption is quite realistic, especially when thesystem is too complicated or constantly changing. Nodes may exchange theobservation of their local utilities to estimate the global utility at eachtimeslot. We propose stochastic perturbation based distributed algorithms underthe assumptions whether each node has collected local utilities of all or onlypart of the other nodes. We use tools from stochastic approximation to provethat both algorithms converge to the optimum. The convergence rate of thealgorithms is also derived. Although the proposed algorithms can be applied togeneral optimization problems, we perform simulations considering power controlin wireless networks and present numerical results to corroborate our claim.

Distributed Stochastic Optimization in Networks with Low Informational Exchange