Title :

Differentially Private Best-Arm Identification

Author(s) :

Azize, Achraf [Auteur]
Scool [Scool]
Jourdan, Marc [Auteur]
Scool [Scool]
Marjani, Aymen Al [Auteur]
École normale supérieure de Lyon [ENS de Lyon]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Basu, Debabrota [Auteur]
Centrale Lille
Université de Lille
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Scool [Scool]

Publication date :

2024-06-10

English keyword(s) :

Differential privacy
Bandit
Best arm identification
Sample complexity
Fixed confidence best-arm identification
Local differential privacy
Lower bounds

HAL domain(s) :

Statistiques [stat]/Machine Learning [stat.ML]
Informatique [cs]/Intelligence artificielle [cs.AI]
Informatique [cs]/Cryptographie et sécurité [cs.CR]
Informatique [cs]/Apprentissage [cs.LG]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies. Motivated by the data privacy ...
Show more >Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies. Motivated by the data privacy concerns invoked by these applications, we study the problem of BAI with fixed confidence in both the local and central models, i.e. $\epsilon$-local and $\epsilon$-global Differential Privacy (DP). First, to quantify the cost of privacy, we derive lower bounds on the sample complexity of any $\delta$-correct BAI algorithm satisfying $\epsilon$-global DP or $\epsilon$-local DP. Our lower bounds suggest the existence of two privacy regimes. In the high-privacy regime, the hardness depends on a coupled effect of privacy and novel information-theoretic quantities involving the Total Variation. In the low-privacy regime, the lower bounds reduce to the non-private lower bounds. We propose $\epsilon$-local DP and $\epsilon$-global DP variants of a Top Two algorithm, namely CTB-TT and AdaP-TT*, respectively. For $\epsilon$-local DP, CTB-TT is asymptotically optimal by plugging in a private estimator of the means based on Randomised Response. For $\epsilon$-global DP, our private estimator of the mean runs in arm-dependent adaptive episodes and adds Laplace noise to ensure a good privacy-utility trade-off. By adapting the transportation costs, the expected sample complexity of AdaP-TT* reaches the asymptotic lower bound up to multiplicative constants.Show less >

Language :

Anglais

ANR Project :

REPUBLIC: Vers l'IA responsable avec l'apprentissage par renforcement sous contraintes
Foundations of robustness and reliability in artificial intelligence
Programme de formation doctorale en IA à Lille
Apprentissage séquentiel et actif pour l'optimisation

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL