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Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
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| Citations: | 125 - 13 self |
BibTeX
@MISC{Srinivas_gaussianprocess,
author = {Niranjan Srinivas and Andreas Krause and Matthias Seeger},
title = {Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design},
year = {}
}
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Abstract
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 RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches. 1.
Keyphrases
experimental design bandit setting gaussian process optimization gp optimization cumulative regret gaussian process many application payoff function covariance function important case novel convergence rate important open problem explicit sublinear regret bound novel connection regret bound real sensor data noisy function maximal information gain operator spectrum intuitive upper-confidence weak dependence heuristical gp optimization approach low rkhs norm multiarmed bandit problem
