Title :

Statistical efficiency of Thompson sampling for combinatorial semi-bandits

Author(s) :

Perrault, Pierre [Auteur]
Scool [Scool]
Ecole Normale Supérieure Paris-Saclay [ENS Paris Saclay]
Boursier, Etienne [Auteur]
Ecole Normale Supérieure Paris-Saclay [ENS Paris Saclay]
Perchet, Vianney [Auteur]
Centre de Recherche en Économie et Statistique [CREST]
Criteo AI Lab
Valko, Michal [Auteur]
DeepMind [Paris]

Conference title :

Neural Information Processing Systems

City :

Virtual

Country :

France

Start date of the conference :

2020-12-06

HAL domain(s) :

Informatique [cs]/Intelligence artificielle [cs.AI]
Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic ...
Show more >We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in $[0,1]$, we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

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

Source :

Harvested from HAL