Explore First, Exploit Next: The True Shape of Regret in Bandit Problems

Abstract : We revisit lower bounds on the regret in the case of multi-armed bandit problems. We obtain non-asymptotic, distribution-dependent bounds and provide straightforward proofs based only on well-known properties of Kullback-Leibler divergences. These bounds show in particular that in an initial phase the regret grows almost linearly, and that the well-known logarithmic growth of the regret only holds in a final phase. The proof techniques come to the essence of the information-theoretic arguments used and they are deprived of all unnecessary complications.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01276324
Contributeur : Gilles Stoltz <>
Soumis le : lundi 8 octobre 2018 - 22:02:31
Dernière modification le : samedi 27 octobre 2018 - 01:21:21

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Bandit-lower-bounds-MOR-v3.pdf
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Aurélien Garivier, Pierre Ménard, Gilles Stoltz. Explore First, Exploit Next: The True Shape of Regret in Bandit Problems. 2017. 〈hal-01276324v3〉

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