A penalized bandit algorithm

Damien Lamberton (1) , Gilles Pagès (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study a two armed-bandit algorithm with penalty. We show the convergence of the algorithm and establish the rate of convergence. For some choices of the parameters, we obtain a central limit theorem in which the limit distribution is characterized as the unique stationary distribution of a discontinuous Markov process.

Mots clés: Two-armed bandit algorithm; Stochastic Approximation; learning automata; asset allocation

Domaines: Probabilités [math.PR]

Damien Lamberton, Gilles Pagès. A penalized bandit algorithm. Electronic Journal of Probability, 2008, 13, 341-373 ; http://dx.doi.org/10.1214/EJP.v13-489. ⟨10.1214/EJP.v13-489⟩. ⟨hal-00012187⟩