This paper addresses a distributed optimization problem in a large communication network, where nodes are active sporadically. Each active node should properly control its action to maximize the global performance of the network, which is characterized by a pre-defined utility function. We consider a challenging situation where the optimization algorithm has to be performed only based on a scalar approximation of the utility function, rather than its closed-form expression, so that the typical gradient descent method cannot be applied. This setting is quite realistic when the network is affected by some stochastic and time-varying process, and that each node cannot have the full knowledge of the network states. We propose a distributed optimization algorithm and proves its almost surely convergence to the optimum. Numerical results are also presented to justify our claim.