Stochastic optimal control with neural networks and application to a retailer inventory problem

Overwhelming computational requirements of classical dynamic programming algorithms render them inapplicable to most practical stochastic problems. To overcome this problem a neural network based Dynamic Programming (DP) approach is described in this study. The cost function which is critical in a dynamic programming formulation is approximated by a neural network according to some designed weight-update rule based on Temporal Difference (TD) learning. A Lyapunov based theory is developed to guarantee an upper error bound between the output of the cost neural network and the true cost. We illustrate this approach through a retailer inventory problem.