Absfracf-The shortest path problem on stochastic graphs is addressed. A stochastic optimal control problem is slated, for which dynamic programming can be used. The complexity of the problem leads us tu look for a suboptimal solution making use of neural networks to approximate the cost-togo function. By introducing the concept of "frontier", an alternative technique is given, for which any feasible policy leads to the destination node. Moreover by using a suitable algorithm, any approximation of the cost-to-go function can he used to obtain a proper policy. Barron's results suggest the method might nut incur the "curse of dimensionality".