Stability of stochastic optimization problems - nonmeasurable case

Petr Lachout

Kybernetika (2008)

  • Volume: 44, Issue: 2, page 259-276
  • ISSN: 0023-5954

Abstract

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This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, ε -optimal solutions are considered. The setup is illustrated on consistency of a ε - M -estimator in linear regression model.

How to cite

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Lachout, Petr. "Stability of stochastic optimization problems - nonmeasurable case." Kybernetika 44.2 (2008): 259-276. <http://eudml.org/doc/33925>.

@article{Lachout2008,
abstract = {This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, $\varepsilon $-optimal solutions are considered. The setup is illustrated on consistency of a $\varepsilon $-$M$-estimator in linear regression model.},
author = {Lachout, Petr},
journal = {Kybernetika},
keywords = {stability of stochastic optimization problem; weak convergence of probability measures; estimator consistency; metric spaces; stability of stochastic optimization problem; weak convergence of probability measures; estimator consistency; metric spaces},
language = {eng},
number = {2},
pages = {259-276},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability of stochastic optimization problems - nonmeasurable case},
url = {http://eudml.org/doc/33925},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Lachout, Petr
TI - Stability of stochastic optimization problems - nonmeasurable case
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 2
SP - 259
EP - 276
AB - This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, $\varepsilon $-optimal solutions are considered. The setup is illustrated on consistency of a $\varepsilon $-$M$-estimator in linear regression model.
LA - eng
KW - stability of stochastic optimization problem; weak convergence of probability measures; estimator consistency; metric spaces; stability of stochastic optimization problem; weak convergence of probability measures; estimator consistency; metric spaces
UR - http://eudml.org/doc/33925
ER -

References

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