Two-Target Algorithms for Infinite-Armed Bandits with Bernoulli Rewards - Archive ouverte HAL Access content directly
Conference Papers Year : 2013

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

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Thomas Bonald
• Function : Correspondent author
• PersonId : 3160
• IdHAL : tbonald
• IdRef : 12422959X

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Alexandre Proutière
• Function : Author
• PersonId : 833456

#### 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.

#### Domains

Computer Science [cs] Machine Learning [cs.LG]
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### Dates and versions

hal-00920045 , version 1 (17-12-2013)

### Identifiers

• HAL Id : hal-00920045 , version 1

### Cite

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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