Monte Carlo Minimization for Sequential Control
by Li-Shya Chen, Seymour Geisser, Charles J. Geyer
Technical Report No. 591
School of Statistics
University of Minnesota
August, 1993
Research supported in part by NIGMS Grant GM 25271.
Research supported in part by NSF Grant DMS-9007833.
Abstract
Sequential updating solutions to optimal control problems are typically not
available in closed form. Here we present a method of Monte Carlo calculation
of sequential updating solutions by simulating realizations from the
predictive expected loss (p.e.l.) by averaging over the simulations. The
minimizer of the approximate p.e.l. is taken to approximate the exact p.e.l.
The approximate minimizer is shown to converge to the exact minimizer under
very weak regularity conditions (mere 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
autogressive responses (ARX) and from dynamic input-output models using a
variety of loss functions.