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CATEGORIES:Machine Learning @ CUED
SUMMARY:Gaussian Process Optimization in the Bandit Settin
 g: No Regret and Experimental Design - Andreas Kra
 use (Caltech)
DTSTART;TZID=Europe/London:20100707T110000
DTEND;TZID=Europe/London:20100707T120000
UID:TALK25444AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25444
DESCRIPTION:Many applications require optimizing an unknown\, 
 noisy function that is expensive to\nevaluate. We 
 formalize this task as a multi-\narmed bandit prob
 lem\, where the payoff function\nis either sample
 d from a Gaussian process (GP)\nor has low RKHS no
 rm. We resolve the important open problem of deriv
 ing regret bounds for\nthis setting\, which imply 
 novel convergence rates\nfor GP optimization. We a
 nalyze GP-UCB\, an\nintuitive upper-condence base
 d algorithm\, and\nbound its cumulative regret in 
 terms of maximal\ninformation gain\, establishing 
 a novel connection\nbetween GP optimization and ex
 perimental design. Moreover\, by bounding the latt
 er in terms\nof operator spectra\, we obtain expli
 cit sublinear\nregret bounds for many commonly use
 d covariance functions. In some important cases\, 
 our\nbounds have surprisingly weak dependence on\n
 the dimensionality. In our experiments on real\nse
 nsor data\, GP-UCB compares favorably with\nother 
 heuristical GP optimization approaches.
LOCATION:Engineering Department\, CBL Room 438
CONTACT:Peter Orbanz
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