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SUMMARY:Highly-Smooth Zero-th Order Online Optimization - Vianney Perchet 
 (INRIA &amp\; Paris Diderot)
DTSTART:20151030T160000Z
DTEND:20151030T170000Z
UID:TALK60700@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:The minimization of convex functions which are only available 
 through partial and noisy information is a key methodological problem in m
 achine learning. We consider  online convex optimization with noisy zero-t
 h order information\, that is noisy function evaluations at any desired po
 int. We focus on problems with high degrees of smoothness\, such as online
  logistic regression. We show that as opposed to gradient-based algorithms
 \, high-order smoothness may be used to improve estimation rates\, with a 
 precise dependence  of our upper-bounds on the degree of smoothness. In pa
 rticular\, we show that for infinitely differentiable functions\, we recov
 er essentially the same dependence on sample size as gradient-based algori
 thms\, with an extra dimension-dependent factor. This is done for convex a
 nd strongly-convex functions\, with finite horizon and anytime algorithms.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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