Distributed resource allocation over random networks based on stochastic approximation

In this paper, we study a resource allocation problem in which a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint and allocation feasibility constraints, where the global objective function is the sum of agents' local objective functions. Each agent can only get noisy observations of its local gradient function and its local resource, which cannot be shared by other agents or transmitted to a center. There also exist communication uncertainties such as time-varying topologies (described by random graphs) and additive channel noises. To solve the resource allocation with uncertainties, we propose a stochastic approximation based distributed algorithm, and prove that agents can collaboratively achieve the optimal allocation with probability one by virtue of the ordinary differential equation (ODE) method for stochastic approximation. Finally, simulations related to the demand response management in power systems verify the effectiveness of the proposed algorithm.