Upper-Confidence-Bound Algorithms for Active Learning in Multi-Armed Bandits

Alexandra Carpentier 1 Alessandro Lazaric 1 Mohammad Ghavamzadeh 1 Rémi Munos 1 Peter Auer 2
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
Abstract : In this paper, we study the problem of estimating the mean values of all the arms uniformly well in the multi-armed bandit setting. If the variances of the arms were known, one could design an optimal sampling strategy by pulling the arms proportionally to their variances. However, since the distributions are not known in advance, we need to design adaptive sampling strategies to select an arm at each round based on the previous observed samples. We describe two strategies based on pulling the arms proportionally to an upper-bound on their variances and derive regret bounds for these strategies. %on the excess estimation error compared to the optimal allocation. We show that the performance of these allocation strategies depends not only on the variances of the arms but also on the full shape of their distributions.
Complete list of metadatas

https://hal.inria.fr/hal-00659696
Contributor : Alexandra Carpentier <>
Submitted on : Friday, January 13, 2012 - 2:46:53 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM
Long-term archiving on : Monday, November 19, 2012 - 1:35:39 PM

File

adapt_alloc_tech-report.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00659696, version 1

Collections

Citation

Alexandra Carpentier, Alessandro Lazaric, Mohammad Ghavamzadeh, Rémi Munos, Peter Auer. Upper-Confidence-Bound Algorithms for Active Learning in Multi-Armed Bandits. ALT - the 22nd conference on Algorithmic Learning Theory, Oct 2011, Espoo, Finland. ⟨hal-00659696⟩

Share

Metrics

Record views

918

Files downloads

1748