  In this paper, a stochastic approximation (SA) based distributed algorithm is
proposed to solve the resource allocation (RA) with uncertainties. In this
problem, 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
function's gradient and its local resource, which cannot be shared by other
agents or transmitted to a center. 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 prove that agents can collaboratively achieve the optimal
allocation with probability one by virtue of ordinary differential equation
(ODE) method for SA. Finally, simulations related to the demand response
management in power systems verify the effectiveness of the proposed algorithm.
