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High-probability regret bounds for bandit online linear optimization

Bartlett, Peter L., Dani, Varsha, Hayes, Thomas, Kakade, Sham, Rakhlin, Alexander, & Tewari, Ambuj (2008) High-probability regret bounds for bandit online linear optimization. In 21th Annual Conference on Learning Theory (COLT 2008), 9-12 July 2008, Helsinki, Finland.

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Abstract

We present a modification of the algorithm of Dani et al. [8] for the online linear optimization problem in the bandit setting, which with high probability has regret at most O ∗ ( √ T) against an adaptive adversary. This improves on the previous algorithm [8] whose regret is bounded in expectation against an oblivious adversary. We obtain the same dependence on the dimension (n 3/2) as that exhibited by Dani et al. The results of this paper rest firmly on those of [8] and the remarkable technique of Auer et al. [2] for obtaining high probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings.

Impact and interest:

11 citations in Scopus
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ID Code: 45706
Item Type: Conference Paper
Keywords: algorithm, linear optimization, high probability
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > INFORMATION SYSTEMS (080600)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2008 [please consult the authors]
Deposited On: 06 Sep 2011 08:16
Last Modified: 08 Sep 2011 17:30

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