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SUMMARY:Gaussian Process Optimization in the Bandit Setting: No Regret and
  Experimental Design - Andreas Krause (Caltech)
DTSTART:20100707T100000Z
DTEND:20100707T110000Z
UID:TALK25444@talks.cam.ac.uk
CONTACT:Peter Orbanz
DESCRIPTION:Many applications require optimizing an unknown\, noisy functi
 on that is expensive to\nevaluate. We formalize this task as a multi-\narm
 ed bandit problem\, where the payoff function\nis either sampled from a G
 aussian process (GP)\nor has low RKHS norm. We resolve the important open 
 problem of deriving regret bounds for\nthis setting\, which imply novel co
 nvergence rates\nfor GP optimization. We analyze GP-UCB\, an\nintuitive up
 per-condence based algorithm\, and\nbound its cumulative regret in terms 
 of maximal\ninformation gain\, establishing a novel connection\nbetween GP
  optimization and experimental design. Moreover\, by bounding the latter i
 n terms\nof operator spectra\, we obtain explicit sublinear\nregret bounds
  for many commonly used covariance functions. In some important cases\, ou
 r\nbounds have surprisingly weak dependence on\nthe dimensionality. In our
  experiments on real\nsensor data\, GP-UCB compares favorably with\nother 
 heuristical GP optimization approaches.
LOCATION:Engineering Department\, CBL Room 438
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