First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper under review'Predictive Entropy Search for Efficient Global Optimization of Black-box Functions' presents an approach for Bayesian optimization that measures entropy in the posterior predictive distribution. The authors present a method named Predictive Entropy Search (PES) that is derived by a reparameterization of the expected information gain based on the symmetry of mutual information. The authors describe the posterior sampling, predictive entropy approximation and hyper-parameter learning steps of PES. The advantages of the proposed method are that it is more efficient and accurate than alternatives and that it allows to handle the hyper-parameters in a fully Bayesian way.

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 hy-perparameters 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.

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.

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 realworld 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.

Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the hyper-parameter tuning problem of machine learning models. Bayesian optimization is a class of methods with state-of-the-art performance delivering a solution to this problem in real scenarios. It uses an iterative process that employs a probabilistic surrogate model, typically a Gaussian process, of the objective function to be optimized computing a posterior predictive distribution of the black-box function. Based on the information given by this posterior predictive distribution, Bayesian optimization includes the computation of an acquisition function that represents, for every input space point, the utility of evaluating that point in the next iteraiton if the objective of the process is to retrieve a global extremum. This paper is a survey of the information theoretical acquisition functions, whose performance typically outperforms the rest of acquisition functions. The main concepts of the field of information theory are also described in detail to make the reader aware of why information theory acquisition functions deliver great results in Bayesian optimization and how can we approximate them when they are intractable. We also cover how information theory acquisition functions can be adapted to complex optimization scenarios such as the multi-objective, constrained, non-myopic, multi-fidelity, parallel and asynchronous settings and provide further lines of research.

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 propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.

This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. PESMOC can hence be used to solve a wide range of optimization problems. Iteratively, PESMOC chooses an input location on which to evaluate the objective functions and the constraints so as to maximally reduce the entropy of the Pareto set of the corresponding optimization problem. The constraints considered in PESMOC are assumed to have similar properties to those of the objective functions in typical Bayesian optimization problems. That is, they do not have a known expression (which prevents gradient computation), their evaluation is considered to be very expensive, and the resulting observations may be corrupted by noise. These constraints arise in a plethora of expensive black-box optimization problems. We carry out synthetic experiments to illustrate the effectiveness of PESMOC, where we sample both the objectives and the constraints from a Gaussian process prior. The results obtained show that PESMOC is able to provide better recommendations with a smaller number of evaluations than a strategy based on random search.

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.

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.