  We propose a novel information-theoretic approach for Bayesian optimization
called Predictive Entropy Search (PES). At each iteration, PES selects the next
evaluation point that maximizes the expected information gained with respect to
the global maximum. PES codifies this intractable acquisition function in terms
of the expected reduction in the differential entropy of the predictive
distribution. This reformulation allows PES to obtain approximations that are
both more accurate and efficient than other alternatives such as Entropy Search
(ES). Furthermore, PES can easily perform a fully Bayesian treatment of the
model hyperparameters while ES cannot. We evaluate PES in both synthetic and
real-world applications, including optimization problems in machine learning,
finance, biotechnology, and robotics. We show that the increased accuracy of
PES leads to significant gains in optimization performance.
