Title :

On the Complexity of Best Arm Identification in Multi-Armed Bandit Models

Author(s) :

Kaufmann, Emilie [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Sequential Learning [SEQUEL]
Cappé, Olivier [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Garivier, Aurélien [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Journal title :

Journal of Machine Learning Research

Pages :

1-42

Publisher :

Microtome Publishing

Publication date :

2016-01-01

ISSN :

1532-4435

English keyword(s) :

multi-armed bandit
best arm identification
pure exploration
information-theoretic divergences
sequential testing

HAL domain(s) :

Statistiques [stat]/Machine Learning [stat.ML]

English abstract : [en]

The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well ...
Show more >The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identifying the m best arms. We introduce generic notions of complexity for the two dominant frameworks considered in the literature: fixed-budget and fixed-confidence settings. In the fixed-confidence setting, we provide the first known distribution-dependent lower bound on the complexity that involves information-theoretic quantities and holds when m is larger than 1 under general assumptions. In the specific case of two armed-bandits, we derive refined lower bounds in both the fixed-confidence and fixed-budget settings, along with matching algorithms for Gaussian and Bernoulli bandit models. These results show in particular that the complexity of the fixed-budget setting may be smaller than the complexity of the fixed-confidence setting, contradicting the familiar behavior observed when testing fully specified alternatives. In addition, we also provide improved sequential stopping rules that have guaranteed error probabilities and shorter average running times. The proofs rely on two technical results that are of independent interest : a deviation lemma for self-normalized sums (Lemma 19) and a novel change of measure inequality for bandit models (Lemma 1).Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Statistique Semi-Paramétrique pour l'Allocation Dynamique de Ressources et l'Optimisation
Apprentissage Adaptatif pour le Crowdsourcing Intelligent et l'Accès à l'Information

Collections :

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

Source :

Harvested from HAL