Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many…

• NS
  National Science Foundation

  Award: 0932392
• M
  Microsoft
• DF
  Deutsche Forschungsgemeinschaft
• OO
  Office of Naval Research

  Awards: N00014-09-1-1044, N00014