When can the two-armed bandit algorithm be trusted?
By Damien Lamberton, Gilles Pagès, Pierre Tarres. 2004
47 citations recorded by the source corpus.
We investigate the asymptotic behaviour of one version 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.
Subfields: Artificial Intelligence, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/beb078b16adf85ccaf9fcf7de66c4bcdd314cf06
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In Artificial Intelligence
In Management Science and Operations Research
Citations in the corpus
- A survey of random processes with reinforcement (2006, background): “uilibrium at 1. The attractor must be the limit of {Xn} with positive probability, but can the repeller be the limit with positive probability? The answer depends on the sequence {γn}. It is shown in [LPT04] that for γn ∼ n−α, the repeller can be a limit with positive probability when α < 1. Inde”