Shortest path problems on stochastic graphs: a neuro dynamic programming approach

The shortest path problem on stochastic graphs is addressed. A stochastic optimal control problem is stated, for which dynamic programming can be used. The complexity of the problem leads us to look for a suboptimal solution making use of neural networks to approximate the cost-to-go 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 be used to obtain a proper policy. Barron's results suggest the method might not incur the "curse of dimensionality".