- A short (4 page) paper
- Analysis of upper confidence bound on Gaussian process optimization
- Smootheness is encoded by covariance function
- The Gaussian Bandit UCB requires a discrete set of test points, which seems strange
- There are some notation abuses that are difficult to understand, for example their definition of a no-regret algorithm and the statement that UCB is a no regret algorithm
- The regret bound in discrete UCB is O(sqrt(kt)). For the infinite arm case, K is replaced by the bound for the maximum possible information gain due to sampling
- The say this connects GP optimization w/ optimal experimental design, should read more about this
- Here there is noise on the reward observations, it is assumed to be Gaussian
- Although it is a regret algorithm it looks like there is a probability of failure delta
- Information gain is submodular – more information is gained when the total number of points sampled is low (although there has to be cases where this isn’t true)
- There is a different regret bound here that also has sqrtish flavor

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