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arXiv · 1602.07182

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

Aurélien Garivier·Pierre Ménard·Gilles Stoltz
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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.

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Aurélien Garivier, Pierre Ménard, Gilles Stoltz. 2016-02-23. Explore First, Exploit Next: The True Shape of Regret in Bandit Problems. https://arxiv.org/abs/1602.07182

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