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Summary: Algorithms for Infinitely Many-Armed Bandit
(Supplementary file)
Yizao Wang
INRIA Futurs Lille, SequeL project,
40 avenue Halley, 59650 Villeneuve d'Ascq, France
yizwang@umich.edu
Jean-Yves Audibert
Université Paris Est, Ecole des Ponts, ParisTech, Certis
& Willow - ENS / INRIA, Paris, France
audibert@certis.enpc.fr
Rémi Munos
INRIA Futurs Lille, SequeL project,
40 avenue Halley, 59650 Villeneuve d'Ascq, France
remi.munos@inria.fr
Theorem 3 Any algorithm suffers a regret larger than cn
1+ for some small enough constant c
depending on c2 and .
Proof of Theorem 3. An elementary event of the probability space is characterized by the infinite
sequence I1, I2, . . . of arms and by the infinite sequences of rewards corresponding to each of the
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