Near optimal stochastic solutions to uncertain least square problems

Author

Calafiore, Giuseppe ; Dabbene, Fabrizio

Author_Institution

Dipt. di Autom. e Informatica, Politecnico di Torino, Italy

Volume

5

fYear

2003

fDate

4-6 June 2003

Firstpage

3803

Abstract

In this paper, we present a recursive algorithm for the solution of uncertain least-square problems in a stochastic setting. The algorithm aims at minimizing the expected value with respect to the uncertainty of the least-square residual, and returns with high probability an ε-suboptimal solution in a pre-specified number of iterations. The proposed technique is based on minimization of the empirical mean and on uniform convergence results derived from learning theory inequalities. Comparisons with gradient algorithms for stochastic optimization are also discussed in the paper.

Keywords

learning (artificial intelligence); least squares approximations; recursive estimation; stochastic processes; uncertain systems; ε-suboptimal solution; empirical mean minimization; gradient algorithm; learning theory; recursive algorithm; stochastic optimisation; stochastic solution; uncertain least square problem; uniform convergence; Ear; Equations; Fires; Least squares methods; Resonance light scattering; Robustness; Stochastic processes; Stochastic systems; Uncertainty; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1240427

Filename

1240427