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.
We present a modification of the algorithm of Dani et al.  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  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  and the remarkable technique of Auer et al.  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.
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|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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