Decomposition-Coordination Method for Finite Horizon Bandit Problems - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Decomposition-Coordination Method for Finite Horizon Bandit Problems

Michel de Lara
Benjamin Heymann
  • Fonction : Auteur
Jean-Philippe Chancelier
  • Fonction : Auteur

Résumé

Optimally solving a multi-armed bandit problem suffers the curse of dimensionality. Indeed, resorting to dynamic programming leads to an exponential growth of computing time, as the number of arms and the horizon increase. We introduce a decompositioncoordination heuristic, DeCo, that turns the initial problem into parallelly coordinated one-armed bandit problems. As a consequence, we obtain a computing time which is essentially linear in the number of arms. In addition, the decomposition provides a theoretical lower bound on the regret. For the two-armed bandit case, dynamic programming provides the exact solution, which is almost matched by the DeCo heuristic. Moreover, in numerical simulations with up to 100 rounds and 20 arms, DeCo outperforms classic algorithms (Thompson sampling and Kullback-Leibler upper-confidence bound) and almost matches the theoretical lower bound on the regret for 20 arms.
Fichier principal
Vignette du fichier
preprint_bandit_decomposition_v1.pdf (403.65 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03240964 , version 1 (01-06-2021)

Identifiants

Citer

Michel de Lara, Benjamin Heymann, Jean-Philippe Chancelier. Decomposition-Coordination Method for Finite Horizon Bandit Problems. 2021. ⟨hal-03240964⟩
78 Consultations
39 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More