eprintid: 1715
rev_number: 6
eprint_status: archive
userid: 46
dir: disk0/00/00/17/15
datestamp: 2013-09-13 10:30:44
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-13 10:30:44
type: article
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: Suboptimal Solutions to Dynamic Optimization Problems via Approximations of the Policy Functions
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Dynamic optimization; Dynamic programming; Suboptimal policies; Approximation schemes; Curse of dimensionality
abstract: The approximation of the optimal policy functions is investigated for dynamic optimization problems with an objective that is additive over a finite number of stages. The distance between optimal and suboptimal values of the objective functional is estimated, in terms of the errors in approximating the optimal policy functions at the various stages. Smoothness properties are derived for such functions and exploited to choose the approximating families. The approximation error is measured in the supremum norm, in such a way to control the error propagation from stage to stage. Nonlinear approximators corresponding to Gaussian radial-basis-function networks with adjustable centers and widths are considered. Conditions are defined, guaranteeing that the number of Gaussians (hence, the number of parameters to be adjusted) does not grow “too fast” with the dimension of the state vector. The results help to mitigate the curse of dimensionality in dynamic optimization. An example of application is given and the use of the estimates is illustrated via a numerical simulation.
date: 2010
date_type: published
publication: Journal of Optimization Theory and Applications
volume: 146
number: 3
publisher: Springer-Verlag
pagerange: 764-794
id_number: 10.1007/s10957-010-9680-7
refereed: TRUE
issn: 0022-3239
official_url: http://dx.doi.org/10.1007/s10957-010-9680-7
projects: Partially supported by a grant “Progetti di Ricerca di Ateneo 2008” of the University of Genoa, Project “Solution of Functional Optimization Problems by Nonlinear Approximators and Learning from Data”
citation:   Gnecco, Giorgio and Sanguineti, Marcello  Suboptimal Solutions to Dynamic Optimization Problems via Approximations of the Policy Functions.  Journal of Optimization Theory and Applications, 146 (3).  pp. 764-794.  ISSN 0022-3239      (2010)