  We consider the framework of convex high dimensional stochastic control
problems, in which the controls are aggregated in the cost function. As first
contribution, we introduce a modified problem, whose optimal control is under
some reasonable assumptions an $\varepsilon$-optimal solution of the original
problem. As second contribution, we present a decentralized algorithm whose
convergence to the solution of the modified problem is established. Finally, we
study the application of the developed tools in an engineering context,
studying a coordination problem for large populations of domestic
thermostatically controlled loads (TCLs)
