Geodesic
Learning the distribution with largest mean: two bandit frameworks
ESAIM. Proceedings, Tome 60 (2017), pp. 114-131.

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Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential learning tasks that have been considered in the bandit literature ; they can be formulated as (sequentially) learning which distribution has the highest mean among a set of distributions, with some constraints on the learning process. For both of them (regret minimization and best arm identification) we present recent, asymptotically optimal algorithms. We compare the behaviors of the sampling rule of each algorithm as well as the complexity terms associated to each problem. 
@article{EP_2017_60_a6,
     author = {Emilie Kaufmann and Aur\'elien Garivier},
     title = {Learning the distribution with largest mean: two bandit frameworks},
     journal = {ESAIM. Proceedings},
     pages = {114--131},
     publisher = {mathdoc},
     volume = {60},
     year = {2017},
     doi = {10.1051/proc/201760114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201760114/}
}
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Emilie Kaufmann; Aurélien Garivier. Learning the distribution with largest mean: two bandit frameworks. ESAIM. Proceedings, Tome 60 (2017), pp. 114-131. doi : 10.1051/proc/201760114. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760114/

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