Orthogonalized dynamic programming state space for efficient value function approximation

Dynamic programming (DP) is a mathematical programming method for optimizing a system changing over time and has been used to solve multi-stage optimization problems in manufacturing systems, environmental engineering, and many other fields. Exact solutions are only possible for small problems or under very limiting restrictions. Given recent advances in computational power, approximate DP (ADP) methods now exist; however, they are still subject to the "curse of dimensionality" and rendered computationally intractable in high-dimensions, with few exceptions. In addition, most continuous-state problems require an approximate solution through discretization of the state space. By incorporating a design and analysis of computer experiments (DACE) approach, which uses experimental design and statistical modeling to efficiently represent computer experiment output, computationallytractable ADP methods for continuous-state problems are possible. However, ideal experimental designs are orthogonal, and when the state variables are correlated, ideal experimental designs will not appropriately represent the state space. Data mining methods are employed in this study for two purposes: (1) to orthogonalize a DP state space and enable the use of ideal experimental designs, and (2) to reduce the dimensionality of a DP problem. Results are presented for an Atlanta ozone pollution problem.