Publication

On L2-Regularization for Virtual Reference Feedback Tuning

Alireza Karimi
2013
Conference Papers

Résumé

The Virtual Reference Feedback Tuning (VRFT) approach is a design method that allow optimal feedback control laws to be derived from input-output (I/O) data only, without need of a model of the process. A drawback of this methods is that, in its standard formulation, it is not statistically efficient. In this paper, it is shown that it can be reformulated as a L2-regularized optimization problem, by keeping the same assumptions and features, such that its statistical performance can be improved using the same data. A convex optimization method is also introduced to find the best regularization matrix. The proposed strategy is finally tested on a benchmark example in digital control system design.

Source officielle

https://infoscience.epfl.ch/entities/publication/31df2e8c-ca74-47c4-9fc7-810eb6cae34a

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Alireza Karimi
2013
Conference Papers

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/31df2e8c-ca74-47c4-9fc7-810eb6cae34a

À propos de ce résultat

Concepts associés (26)

Régularisation (mathématiques)

vignette|Les courbes bleues et vertes correspondent à deux modèles differents, tous les deux étant des solutions possibles du problème consistant à décrire les coordonnées de tous les points rouges. L'application d'une régularisation favorise le modèle moins complexe correspondant à la courbe verte. Dans le domaine des mathématiques et des statistiques, et plus particulièrement dans le domaine de l'apprentissage automatique, la régularisation fait référence à un processus consistant à ajouter de l'information à un problème, s'il est mal posé ou pour éviter le surapprentissage.

Ridge regression

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.

Elastic net regularization

In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on Use of this penalty function has several limitations. For example, in the "large p, small n" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates.

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