The Relative Gaussian Mechanism and its ...
Type de document :
Communication dans un congrès avec actes
Titre :
The Relative Gaussian Mechanism and its Application to Private Gradient Descent
Auteur(s) :
Hendrikx, Hadrien [Auteur]
Apprentissage de modèles à partir de données massives [Thoth]
Mangold, Paul [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Bellet, Aurelien [Auteur]
Institut Desbrest de santé publique [IDESP]
Médecine de précision par intégration de données et inférence causale [PREMEDICAL]
Apprentissage de modèles à partir de données massives [Thoth]
Mangold, Paul [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Bellet, Aurelien [Auteur]

Institut Desbrest de santé publique [IDESP]
Médecine de précision par intégration de données et inférence causale [PREMEDICAL]
Titre de la manifestation scientifique :
AISTATS 2024 - 27th International Conference on Artificial Intelligence and Statistics
Ville :
Valencia
Pays :
Espagne
Date de début de la manifestation scientifique :
2024-05-02
Titre de l’ouvrage :
PMLR
Date de publication :
2024-08-29
Discipline(s) HAL :
Informatique [cs]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Résumé en anglais : [en]
The Gaussian Mechanism (GM), which consists in adding Gaussian noise to a vector-valued query before releasing it, is a standard privacy protection mechanism. In particular, given that the query respects some L2 sensitivity ...
Lire la suite >The Gaussian Mechanism (GM), which consists in adding Gaussian noise to a vector-valued query before releasing it, is a standard privacy protection mechanism. In particular, given that the query respects some L2 sensitivity property (the L2 distance between outputs on any two neighboring inputs is bounded), GM guarantees Rényi Differential Privacy (RDP). Unfortunately, precisely bounding the L2 sensitivity can be hard, thus leading to loose privacy bounds. In this work, we consider a Relative L2 sensitivity assumption, in which the bound on the distance between two query outputs may also depend on their norm. Leveraging this assumption, we introduce the Relative Gaussian Mechanism (RGM), in which the variance of the noise depends on the norm of the output. We prove tight bounds on the RDP parameters under relative L2 sensitivity, and characterize the privacy loss incurred by using output-dependent noise. In particular, we show that RGM naturally adapts to a latent variable that would control the norm of the output. Finally, we instantiate our framework to show tight guarantees for Private Gradient Descent, a problem that naturally fits our relative L2 sensitivity assumption.Lire moins >
Lire la suite >The Gaussian Mechanism (GM), which consists in adding Gaussian noise to a vector-valued query before releasing it, is a standard privacy protection mechanism. In particular, given that the query respects some L2 sensitivity property (the L2 distance between outputs on any two neighboring inputs is bounded), GM guarantees Rényi Differential Privacy (RDP). Unfortunately, precisely bounding the L2 sensitivity can be hard, thus leading to loose privacy bounds. In this work, we consider a Relative L2 sensitivity assumption, in which the bound on the distance between two query outputs may also depend on their norm. Leveraging this assumption, we introduce the Relative Gaussian Mechanism (RGM), in which the variance of the noise depends on the norm of the output. We prove tight bounds on the RDP parameters under relative L2 sensitivity, and characterize the privacy loss incurred by using output-dependent noise. In particular, we show that RGM naturally adapts to a latent variable that would control the norm of the output. Finally, we instantiate our framework to show tight guarantees for Private Gradient Descent, a problem that naturally fits our relative L2 sensitivity assumption.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Projet ANR :
Collections :
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