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Article Dans Une Revue Machine Learning Année : 2019

Asymptotically Optimal Algorithms for Budgeted Multiple Play Bandits

Résumé

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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Dates et versions

hal-01338733 , version 1 (29-06-2016)
hal-01338733 , version 2 (05-11-2017)
hal-01338733 , version 3 (03-09-2019)

Identifiants

Citer

Alexander Luedtke, Emilie Kaufmann, Antoine Chambaz. Asymptotically Optimal Algorithms for Budgeted Multiple Play Bandits. Machine Learning, 2019, 108 (11), pp.1919-1949. ⟨10.1007/s10994-019-05799-x⟩. ⟨hal-01338733v3⟩
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