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.
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Submitted on : Monday, October 8, 2018 - 10:02:31 PM
Last modification on : Friday, April 12, 2019 - 4:22:52 PM
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Aurélien Garivier, Pierre Ménard, Gilles Stoltz. Explore First, Exploit Next: The True Shape of Regret in Bandit Problems. Mathematics of Operations Research, INFORMS, In press, ⟨10.1287/moor.2017.0928⟩. ⟨hal-01276324v3⟩

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