Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting

@article{Srinivas2012InformationTheoreticRB,
  title={Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting},
  author={Niranjan Srinivas and Andreas Krause and Sham M. Kakade and Matthias W. Seeger},
  journal={IEEE Transactions on Information Theory},
  year={2012},
  volume={58},
  pages={3250-3265}
}
Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low norm in a reproducing kernel Hilbert space. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze an intuitive Gaussian process upper confidence bound (GP-UCB) algorithm… 
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