Quasi-random sampling for approximate dynamic programming

This paper analyzes quasi-random sampling techniques for approximate dynamic programming. Specifically, low-discrepancy sequences and lattice point sets are investigated and compared as efficient schemes for uniform sampling of the state space in high-dimensional settings. The convergence analysis of the approximate solution is provided basing on geometric properties of the two discretization methods. It is also shown that such schemes are able to take advantage of regularities of the value functions, possibly through suitable transformations of the state vector. Simulation results concerning optimal management of a water reservoirs system and inventory control are presented to show the effectiveness of the considered techniques with respect to pure-random sampling.