Predictive Entropy Search for Efficient Global Optimization of Black-box Functions

By José Miguel Hernández-Lobato, Matthew W. Hoffman, Zoubin Ghahramani. 2014

728 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Numerical Analysis, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Management Science and Operations Research

In Numerical Analysis

In Optimization & Training

Citations in the corpus

Hyper-Parameter Optimization: A Review of Algorithms and Applications (2020, background): “In addition to improvement-based policies, knowledge gradient function (Frazier et al., 2009), entropy search function (Hennig and Schuler, 2012), and predictive entropy search function (Hernández-Lobato et al., 2014) have recently been developed to enhance performance over different applications.”
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets (2016, background): “PES refers to the same acquisition function, but uses different approximations to compute it.”
Multi-fidelity Bayesian Optimisation with Continuous Approximations (2017, methodology): “While there are several techniques for BO (de Fre-itas et al., 2012; Hern´andez-Lobato et al., 2014; Jones et al., 1998; Mockus, 1994; Thompson, 1933), our work will build on the Gaussian process upper conﬁdence bound ( GP-UCB ) algorithm of Srinivas et al. (2010).”
A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design (2017, background): “2009) Predictive entropy search (Hernández-Lobato et al. 2014) Model-dependent; global model; minimize prediction response to do local exploitation while maximize prediction variance to do global exploration; trade-off between global & local is automatically determined”
Non-parametric Policy Search with Limited Information Loss (2017, methodology): “These features have been used successfully in various classification and regression tasks (Rahimi and Recht, 2007; Hernández-Lobato et al., 2014; Lu et al., 2016).”
Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space (2017, methodology): “To implement Thompson sampling (TS) with a GP model, we approximate the non-parametric GP with a parametric approximation based on random features, as described in the supplementary material of (Hernández-Lobato et al., 2014).”
Constrained Bayesian Optimization with Noisy Experiments (2017, methodology): “Hern´andez-Lobato et al. (2014) evaluated PESC on unconstrained Branin and Hartmann6 problems, but with a very low noise level: 0.03, whereas in our experiments the noise standard deviation was 5 for Branin and 0.2 for Hartmann6.”
Multi-Information Source Optimization (2016, methodology): “Following a recommendation of Snoek 2016, our implementation MTBO+ uses an improved formulation of the acquisition function given by Hernández-Lobato et al. [2014], Snoek and et al., but otherwise is identical to MTBO; in particular, it uses the statistical model of Swersky et al. [2013].”
Dealing with Categorical and Integer-valued Variables in Bayesian Optimization with Gaussian Processes (2017, background): “PES has been compared to other acquisition function showing improved optimization results.”
The Parallel Knowledge Gradient Method for Batch Bayesian Optimization (2016, background): “In this paper, the discrete set An is not chosen statically, but evolves over time: specifically, we suggest drawing M samples from the global optima of the posterior distribution of the Gaussian process (please refer to [11, 18] for a description of this technique).”
An Entropy Search Portfolio for Bayesian Optimization (2014, methodology): “We use a random set of features to fix a sample f̃ to optimize [2]: αt(x) = f̃ (x) = Φ(x) w where w are random weights and Φ(x) consists of random Fourier features evaluated at x.”
Maximizing acquisition functions for Bayesian optimization (2018, background): “In some cases, this belief is expressed as an explicit ensemble of sample functions [28, 54, 60].”