Authors:
Miguel Martin
;
Antonio Jiménez-Martín
and
Alfonso Mateos
Affiliation:
Universidad Politécnica de Madrid, Spain
Keyword(s):
Multi-armed Bandit Problem, Possibilistic Reward, Numerical Study.
Related
Ontology
Subjects/Areas/Topics:
Decision Analysis
;
Methodologies and Technologies
;
Operational Research
;
Stochastic Processes
Abstract:
Different allocation strategies can be found in the literature to deal with the multi-armed bandit problem under a frequentist view or from a Bayesian perspective. In this paper, we propose a novel allocation strategy, the possibilistic reward method. First, possibilistic reward distributions are used to model the uncertainty about the arm expected rewards, which are then converted into probability distributions using a pignistic probability transformation. Finally, a simulation experiment is carried out to find out the one with the highest expected reward, which is then pulled. A parametric probability transformation of the proposed is then introduced together with a dynamic optimization, which implies that neither previous knowledge nor a simulation of the arm distributions is required. A numerical study proves that the proposed method outperforms other policies in the literature in five scenarios: a Bernoulli distribution with very low success probabilities, with success probabili
ties close to 0.5 and with success probabilities close to 0.5 and Gaussian rewards; and truncated in [0,10] Poisson and exponential distributions.
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