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

Thomas Bonald 1, * Alexandre Proutière 2, 3
* Corresponding author
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
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.
keyword : bandits
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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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