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An Optimal ADP Algorithm for a High-Dimensional Stochastic Control Problem

We propose a provably optimal approximate dynamic programming algorithm for a class of multistage stochastic problems, taking into account that the probability distribution of the underlying stochastic process is not known and the state space is too large to be explored entirely. The algorithm and its proof of convergence rely on the fact that the optimal value functions of the problems within the problem class are concave and piecewise linear. The algorithm is a combination of Monte Carlo simulation, pure exploitation, stochastic approximation and a projection operation. Several applications, in areas like energy, control, inventory and finance, fall under the framework