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Metric Entropy and Gaussian Bandits S. Grunewalder

Summary: Metric Entropy and Gaussian Bandits
S. Gr¨unew¨alder
J.-Y. Audibert
Universit´e Paris-Est
M. Opper
J. Shawe-Taylor
Metric entropy and generic chaining methods are powerful tools from probabil-
ity theory that can be used to study pathwise properties of stochastic processes.
Despite this fact they have largely been ignored in machine learning. We demon-
strate their power in this work in applying them to a bandit problem with a
Gaussian process prior. The difficulty of the setting lies in the fact that we are
dealing with a continuous space of arms and we need to control the supremum of
a reward process on the arms. We apply the so called Dudley integral to reduce
the problem of controlling the supremum of a "difficult" stochastic process to the
problem of bounding a canonical metric that is based solely on the covariance
function (which is an analytical and thus "simple" object). We consider the sce-


Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure


Collections: Computer Technologies and Information Sciences