A comparison of global and semi-local approximation in T-stage stochastic optimization

Abstract

The paper presents a comparison between two different flavors of nonlinear models to be used for the approximate solution of T-stage stochastic optimization (TSO) problems, a typical paradigm of Markovian decision processes. Specifically, the well-known class of neural networks is compared with a semi-local approach based on kernel functions, characterized by less demanding computational requirements. To this purpose, two alternative methods for the numerical solution of TSO are considered, one corresponding to the classic approximate dynamic programming (ADP) and the other based on a direct optimization of the optimal control functions, introduced here for the first time. Advantages and drawbacks in the TSO context of the two classes of approximators are analyzed, in terms of computational burden and approximation capabilities. Then, their performances are evaluated through simulations in two important high-dimensional TSO test cases, namely inventory forecasting and water reservoirs management.