Distributed Resource Allocation Over Random Networks Based on Stochastic Approximation

In this paper, a distributed algorithm is proposed to solve the resource allocation (RA) under uncertainties based on stochastic approximation (SA) approach. In this problem, a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint, where the global objective function is the sum of agents' local objective functions. Each agent is accessible only to the noisy gradient of its local objective function and its local resource observation, which cannot be shared by other agents or transmitted to a center, and moreover, there are communication uncertainties such as time-varying topologies (described by random graphs) and additive channel noises. To solve the RA, we propose an SA-based distributed algorithm and then prove that it can make the agents collaboratively achieve the optimal allocation with probability one only with their local information, by virtue of ordinary differential equation (ODE) methods for SA. Moreover, a simulation related to the demand response management in power systems verifies the effectiveness of the proposed algorithm.