Min-max hyperparameter tuning, with application to fault detection

Julien Marzat (1, 2, 3) , Hélène Piet-Lahanier (1) , Eric Walter (2)

1 ONERA - The French Aerospace Lab [Palaiseau]
2 L2S - Laboratoire des signaux et systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

In order to reach satisfactory performance, fault diagnosis methods require the tuning of internal parameters, usually called hyperparameters. This is generally achieved by optimizing a performance criterion, typically a trade-off between false-alarm and non-detection rates. Perturbations should also be taken into account, for instance by considering the worst possible case. A new method to achieve such a tuning is described, which is especially interesting when the simulations required are so costly that their number is severely limited. It achieves min-max optimization of the tuning parameters via a relaxation procedure and Kriging-based optimization. This approach is applied to the worst-case optimal tuning of a fault diagnosis method consisting of an observer-based residual generator followed by a statistical test. It readily extends to the tuning of hyperparameters in other contexts.

Keywords: efficient global optimization; expected improvement; fault detection and isolation; Gaussian processes; hyperparameter tuning; Kriging; min-max; worst-case optimization.; worst-case optimization

Domains: Mathematics [math]; Optimization and Control [math.OC]; Engineering Sciences [physics]; Automatic

Julien Marzat, Hélène Piet-Lahanier, Eric Walter. Min-max hyperparameter tuning, with application to fault detection. 18th IFAC World Congress, Aug 2011, Milan, Italy. pp.12904-12909. ⟨hal-00615618⟩