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CATEGORIES:Statistics
SUMMARY:Regret Bounds for Gaussian Process Bandit Problems
- Steffen Grunewalder (University College London)
DTSTART;TZID=Europe/London:20101112T160000
DTEND;TZID=Europe/London:20101112T170000
UID:TALK26723AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26723
DESCRIPTION:\nBandit algorithms are concerned with trading exp
loration with exploitation\nwhere a number of opti
ons are available but we can only learn their qual
ity by\nexperimenting with them. I address the sce
nario in which the reward distribution for\narms i
s modeled by a Gaussian process and there is no no
ise in the observed reward. My\nmain result is a b
ound on the regret experienced by algorithms relat
ive to the a\nposteriori optimal strategy of playi
ng the best arm throughout based on benign\nassump
tions about the covariance function defining the G
aussian process. One of the key\ntools to derive t
he bounds is the Dudley integral which allows to b
ound the expected\nsupremum of a Gaussian Process.
The upper bounds are complemented with correspond
ing\nlower bounds for particular covariance functi
ons demonstrating that in general there is\nat mos
t a logarithmic looseness in the upper bounds. The
bounds are in a sense quite\ncrude as they are ba
sed on an algorithm that samples the whole space u
niformly for the\nmaximum. A better approach would
be to consider an algorithm that pays more attent
ion to\n"high reward plateaus" and study its regre
t. I will discuss this approach and the\ntechnical
problems associated with it in an outlook.\n\n\nh
ttp://www.cs.ucl.ac.uk/people/S.Grunewalder.html
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Richard Nickl
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