Monte Carlo Minimization for one step ahead sequential control

Abstract

Sequential updating solutions to optimal control problems are typically not available in closed form. We present a method of Monte Carlo calculation of sequential one step ahead updating solutions by simulating realizations from the predictive distribution of model parameters and approximating the predictive expected loss (PEL) by averaging over the simulations. The minimizer of the approximate PEL is taken to approximate the exact PEL. The approximate minimizer is shown to converge to the exact minimizer under mere lower semi-continuity of the loss function and is shown to be asymptotically normal under stronger conditions. Examples are given from the problem of controlling a linear regression model with autoregressive responses (ARX) or with autocorrelated errors and from dynamic input-output models using a variety of loss functions.