Output-Space Predictive Entropy Search for Flexible Global Optimization

Recently, a great deal of interest has been paid in the field of Bayesian optimization to methods which take an information-theoretic approach to the design of acquisition functions. Such techniques equate the value of potential query points directly with their information content. The first of these techniques, developed separately as an informational approach to global optimization (IAGO) [9] or entropy search (ES) [3], considers the latent maximizer as a random variable and selects the point which results in the greatest reduction in posterior entropy. The entropy reduction cannot, though, be computed in closed form—as a result these earlier works relied on approximations that are often unwieldy in practice. A more recent formulation due to [4] instead rewrites ES as the mutual information between the latent maximizer and the next observation. This approach, known as predictive entropy search (PES), greatly simplifies the required approximations and allows for further extensions of the optimizer [5].