Asymptotically Optimal Algorithms for Budgeted Multiple Play Bandits release_r6kewsgdjnhadg2f3udztbjeo4

by Alexander Luedtke , Antoine Chambaz

Released as a article .

2017  

Abstract

We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an asymptotic regret lower bound for any uniformly efficient algorithm in our setting. We then study a variant of Thompson sampling for Bernoulli rewards and a variant of KL-UCB for both single-parameter exponential families and bounded, finitely supported rewards. We show these algorithms are asymptotically optimal, both in rate and leading problem-dependent constants, including in the thick margin setting where multiple arms fall on the decision boundary.
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Type  article
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Date   2017-11-06
Version   v2
Language   en ?
arXiv  1606.09388v2
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