High-Probability Regret Bounds for Bandit Online Linear Optimization

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 (n3/2 ) 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 highprobability 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.

• Type: Conference
• Year: 2008
• Where: COLT
• Authors: Peter L. Bartlett, Varsha Dani, Thomas P. Hayes, Sham Kakade, Alexander Rakhlin, Ambuj Tewari
• Keywords: COLT 2008, Dani Et Al, Et Al, Linear Optimization Problem, Machine Learning