Statistical learning control of uncertain systems: theory and algorithms.
type: Item
instance of: scholarly article
title: Statistical learning control of uncertain systems: theory and algorithms.
zbMATH Open document ID: 1052.93066
DOI: 10.1016/S0096-3003(99)00283-0
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: It is well known that control problems can be solved very seldomly exactly. On the other hand, many of the control problems can be reduced to decidability or optimization problems and, moreover, probabilistic methods (based on the Monte Carlo approach) can be employed to solve the new problems approximately. To obtain an accuracy of these methods, the Chernoff Bounds, the Hoeffding Inequality (or generally empirical processes and statistical learning theory) can be employed. However, it is known (from the literature) that a large number of the random samples can only (in this approach) guarantee the accuracy. The authors of the paper suggest another approach. They suggest bootstrap sequential learning algorithms based on Rademacher bootstrap (or other bootstrap techniques). A random number of samples (known as the sample complexity of learning) appears in such algorithms. The theoretical, ``underlying'' assertions are recalled here; however, their proofs can be found in a former paper of V. Koltchinskii, C. T. Adallah and M. Ariola. The introduced algorithm is illustrated on an example, already known from the literature. The paper is written in an understandable way.
Mathematics Subject Classification ID: 93E35
Mathematics Subject Classification ID: 62F40
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 65C60
zbMATH DE Number: 1860862
zbMATH Keywords: bootstrap sequential learning
zbMATH Keywords: Rademacher bootstrap
zbMATH Keywords: sample complexity
author: Vladimir Koltchinskii
author: Chaouki Abdallah
author: M. Ariola
author: Peter Dorato
reviewed by: Vlasta Kaňková
MaRDI profile type: Publication
cites work: Q3286740
cites work: A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
cites work: Q4881152
cites work: Improved sample complexity estimates for statistical learning control of uncertain systems
cites work: A Monte Carlo approach to the analysis of control system robustness
cites work: Q4764177
cites work: Q4261789
cites work: On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
cites work: Q4892198
Wikidata QID: Q127609889
full work available at URL: s0096-3003(99)00283-0
OpenAlex ID: W2043290805
description: scientific article; zbMATH DE number 1860862