# Two-Target Algorithms for Infinite-Armed Bandits with Bernoulli Rewards

* Corresponding author
2 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : We consider an infinite-armed bandit problem with Bernoulli rewards. The mean rewards are independent, uniformly distributed over $[0,1]$. Rewards 0 and 1 are referred to as a success and a failure, respectively. We propose a novel algorithm where the decision to exploit any arm is based on two successive targets, namely, the total number of successes until the first failure and until the first $m$ failures, respectively, where $m$ is a fixed parameter. This two-target algorithm achieves a long-term average regret in $\sqrt{2n}$ for a large parameter $m$ and a known time horizon $n$. This regret is optimal and strictly less than the regret achieved by the best known algorithms, which is in $2\sqrt{n}$. The results are extended to any mean-reward distribution whose support contains 1 and to unknown time horizons. Numerical experiments show the performance of the algorithm for finite time horizons.
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Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00920045
Contributor : Alexandre Proutiere <>
Submitted on : Tuesday, December 17, 2013 - 4:26:27 PM
Last modification on : Friday, December 20, 2019 - 10:14:11 AM
Document(s) archivé(s) le : Saturday, April 8, 2017 - 7:33:11 AM

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• HAL Id : hal-00920045, version 1

### Citation

Thomas Bonald, Alexandre Proutière. Two-Target Algorithms for Infinite-Armed Bandits with Bernoulli Rewards. NIPS 2013 - Neural Information Processing Systems Conference, Dec 2013, Lake Tahoe, Nevada, United States. pp.8. ⟨hal-00920045⟩

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