Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

When can the two-armed bandit algorithm be trusted ?


Code(s) de Classification MSC:

Résumé: We investigate the asymptotic behaviour of the so-called two-armed bandit algorithm. It is an example of stochastic approximation procedure whose associated ODE has both a repulsive and an attractive equilibrium, at which the procedure is noiseless. We show that if the gain parameter is constant or goes to $0$ not too fast, the algorithm does fall in the noiseless repulsive equilibrium with positive probability whereas it always converges to its natural attractive target when the gain parameter goes to zero at some appropriate rates depending on the parameters of the model. We also elucidate the behaviour of the constant step algorithm when the step goes to $0$. Finally, we highlight the connection between the algorithm and the Polya urn. An application to asset allocation is briefly described.

Mots Clés: Two-armed bandit algorithm ; Stochastic Approximation ; learning automata ; Polya urn ; asset allocation

Date: 2002-11-06

Prépublication numéro: PMA-769

Pdf file : PMA-769.pdf