Entropy Search for Information-Efficient Global Optimization

By Philipp Hennig, Christian J. Schuler. 2011

745 citations recorded by the source corpus.

Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corresponding inference problem is intractable in several ways. This paper develops desiderata for probabilistic optimization algorithms, then presents a concrete algorithm which addresses each of the computational intractabilities with a sequence of approximations and explicitly addresses the decision problem of maximizing information gain from each evaluation.

Subfields: Probabilistic & Bayesian Methods, Mathematical Optimization

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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.”
Benchmark and Survey of Automated Machine Learning Frameworks (2019, methodology): “Additionally the acquisition function is enhanced by entropy search (Hennig and Schuler, 2012).”
Survey on Automated Machine Learning (2019, background): “Additionally the acquisition function is enhanced by entropy search (Hennig and Schuler, 2012).”
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets (2016, methodology): “We follow the approach of Hennig and Schuler [24], who approximate p ( f | D ) by a ﬁnite-dimensional Gaussian over an irregular grid of points r 1 , ..., r Z , which are designed heuristically to provide good interpolation resolution on p min .”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, methodology): “Instead of sampling the distribution p (cid:63) ( x | D n ) , entropy search (ES) techniques aim to reduce the uncertainty in the location x (cid:63) by selecting the point that is expected to cause the largest reduction in entropy of the distribution p (cid:63) ( x | D n ) [156], [67], [69].”
Learning to Learn for Global Optimization of Black Box Functions (2016, background): “The idea of applying machine learning techniques to optimize the process of learning itself has a long history [Schmidhuber, 1987, Naik and Mammone, 1992, Thrun and Pratt, 1998].”
Freeze-Thaw Bayesian Optimization (2014, background): “Given a posterior predictive distribution over the minimum, the entropy search [17] approach at each step chooses the input that most reduces expected uncertainty over the location of the minimum.”
Input Warping for Bayesian Optimization of Non-Stationary Functions (2014, background): “…[e.g., Osborne et al., 2009, Brochu et al., 2010, Srinivas et al., 2010, Hutter et al., 2011, Bergstra et al., 2011, Bull, 2011, Snoek et al., 2012, Hennig and Schuler, 2012] in large part due to advances in the ability to efﬁciently and accurately model statistical distributions over large…”
Predictive Entropy Search for Efficient Global Optimization of Black-box Functions (2014, methodology): “For this, we reproduce the within-model comparison experiment described in [9].”
Fast Model Identification via Physics Engines for Data-Efficient Policy Search (2017, methodology): “This is achieved through Entropy Search [Hennig and Schuler, 2012], which explicitly maintains a belief on the optimal parameters.”
Towards efﬁcient Bayesian Optimization for Big Data (2015, methodology): “Therefore, we use entropy search (ES) [11, 12] which aims to decrease the entropy”
Fast Bayesian hyperparameter optimization on large datasets (2017, methodology): “The remainder of the paper is structured as follow: In §2, we review Bayesian optimization, in particular the Entropy Search algorithm (Hennig and Schuler, 2012) on which our method is based.”
Bayesian Optimization for Synthetic Gene Design (2015, background): “The BO framework [14, 3, 10, 6] allows us to explore the gene design space in order to provide rules to build genes with interesting properties, such as genes that are able to produce proteins of interest, or genes able to act on the cell lifespan.”
Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology (2014, background): “Training of autoencoder networks with more than a single hidden layer had been unsuccessful due to the complexity of optimizing the objective until Hinton and Salakhutdinov [2006] demonstrated that unsupervised pre-training, ’stacking’ the weights of restricted Boltzmann machines, provided a good st”
Batch Bayesian Optimization via Local Penalization (2015, background): “A number of possible acquisition functions are now available, ranging from fast heuristics [Osborne, 2010, Jones et al., 1998] to non-local entropy-based approaches [Hennig and Schuler, 2012, Hern´andez-Lobato et al., 2014].”
Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions (2015, methodology): “Significant approximations need to be made to (1) before it becomes practically useful [12].”