In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian Process Mutual Information algorithm (GP-MI), which significantly improves further these upper bounds for the cumulative regret. We confirm the efficiency of this algorithm on synthetic and real tasks against the natural competitor, GP-UCB, and also the Expected Improvement heuristic. Preprint for the 31st International Conference on Machine Learning (ICML 2014) 1 ar X iv :1 31 1. 48 25 v3 [ st at .M L ] 8 J un 2 01 5 Erratum After the publication of our article, we found an error in the proof of Lemma 1 which invalidates the main theorem. It appears that the information given to the algorithm is not sufficient for the main theorem to hold true. The theoretical guarantees would remain valid in a setting where the algorithm observes the instantaneous regret instead of noisy samples of the unknown function. We describe in this page the mistake and its consequences. Let f : X R be the unknown function to be optimized, which is a sample from a Gaussian process. Let's fix x, x1, . . . , xT X and the observations yt = f(xt)+ t where the noise variables t are independent Gaussian noise N (0, ). We define the instantaneous regret rt = f(x?) f(xt) and, MT = T
Gaussian Process Optimization with Mutual Information