## Using Gaussian Processes to Optimize Expensive Functions.

Citations: | 6 - 0 self |

### BibTeX

@MISC{Frean_usinggaussian,

author = {Marcus Frean and Phillip Boyle},

title = {Using Gaussian Processes to Optimize Expensive Functions.},

year = {}

}

### OpenURL

### Abstract

Abstract. The task of finding the optimum of some function f(x) is commonly accomplished by generating and testing sample solutions iteratively, choosing each new sample x heuristically on the basis of results to date. We use Gaussian processes to represent predictions and uncertainty about the true function, and describe how to use these predictions to choose where to take each new sample in an optimal way. By doing this we were able to solve a difficult optimization problem- finding weights in a neural network controller to simultaneously balance two vertical poles- using an order of magnitude fewer samples than reported elsewhere. 1

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Citation Context ...n’s [5] application to one-dimensional curve fitting. Buntine [6], MacKay [7], and Neal [8] introduced a Bayesian interpretation that provided a consistent method for handling network complexity (see =-=[9,10]-=- for reviews), followed by regression in a machine learning context [11–13]. See [14–16] for good introductions. Interesting machine learning applications include reinforcement learning [17], incorpor... |

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Citation Context ...as possible, one solution is to wiggle the poles back and forth about a central position. To prevent this,sGruau [27] defined a fitness function that penalises such solutions, fgruau = 0.1f1 + 0.9f2, =-=[24,26]-=-. The two components are defined over 1000 time steps (10 seconds simulated time): f1 = t/1000 (2) � 0 if t < 100, f2 = 0.75 (3) otherwise. Pt i=t−100 (|xi |+| ˙x i |+|θ1|+| ˙ θ1|) where t is the numb... |

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Citation Context ...tanley and Miikkulainen [24–26]. If the goal is to keep the poles balanced for as long as possible, one solution is to wiggle the poles back and forth about a central position. To prevent this,sGruau =-=[27]-=- defined a fitness function that penalises such solutions, fgruau = 0.1f1 + 0.9f2, [24,26]. The two components are defined over 1000 time steps (10 seconds simulated time): f1 = t/1000 (2) � 0 if t < ... |

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Citation Context ...N}, Gaussian process regression is a machine learning technique for infering likely values of y for a novel input x. The study of Gaussian processes for prediction began in geostatistics with kriging =-=[3]-=-, [4] and O’Hagan’s [5] application to one-dimensional curve fitting. Buntine [6], MacKay [7], and Neal [8] introduced a Bayesian interpretation that provided a consistent method for handling network ... |

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Citation Context ...as possible, one solution is to wiggle the poles back and forth about a central position. To prevent this,sGruau [27] defined a fitness function that penalises such solutions, fgruau = 0.1f1 + 0.9f2, =-=[24,26]-=-. The two components are defined over 1000 time steps (10 seconds simulated time): f1 = t/1000 (2) � 0 if t < 100, f2 = 0.75 (3) otherwise. Pt i=t−100 (|xi |+| ˙x i |+|θ1|+| ˙ θ1|) where t is the numb... |

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Citation Context ...sion in a machine learning context [11–13]. See [14–16] for good introductions. Interesting machine learning applications include reinforcement learning [17], incorporation of derivative observations =-=[18]-=-, speeding up the evaluation of Bayesian integrals [19,20], and as models of dynamical systems [21]. The key assumption is that the posterior distribution p(y|x, D) is Gaussian. To compute its mean an... |

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Citation Context ...f the search surface. Further details are given in [20]. Jones [2] first introduced kriging for optimisation using expected improvement to select the next iterate. Büche, Schraudolph and Koumoutsakos =-=[22]-=- explicitly used Gaussian processes for optimisation, and demonstrated the algorithm’s effectiveness on a number of benchmark problems. This work did not make use of expected improvement, did not plac... |

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(Show Context)
Citation Context ... input x. The study of Gaussian processes for prediction began in geostatistics with kriging [3], [4] and O’Hagan’s [5] application to one-dimensional curve fitting. Buntine [6], MacKay [7], and Neal =-=[8]-=- introduced a Bayesian interpretation that provided a consistent method for handling network complexity (see [9,10] for reviews), followed by regression in a machine learning context [11–13]. See [14–... |

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Citation Context ...gression is a machine learning technique for infering likely values of y for a novel input x. The study of Gaussian processes for prediction began in geostatistics with kriging [3], [4] and O’Hagan’s =-=[5]-=- application to one-dimensional curve fitting. Buntine [6], MacKay [7], and Neal [8] introduced a Bayesian interpretation that provided a consistent method for handling network complexity (see [9,10] ... |

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(Show Context)
Citation Context ...ty (see [9,10] for reviews), followed by regression in a machine learning context [11–13]. See [14–16] for good introductions. Interesting machine learning applications include reinforcement learning =-=[17]-=-, incorporation of derivative observations [18], speeding up the evaluation of Bayesian integrals [19,20], and as models of dynamical systems [21]. The key assumption is that the posterior distributio... |

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(Show Context)
Citation Context ... of using an axis-aligned covariance function to optimise objective functions with correlated output (dependent) variables. The algorithm presented here takes all these factors into account. Recently =-=[28]-=- have used similar ideas to those presented here to optimize the gait of a mobile robot, although they use a different criterion (probability of any improvement) and don’t deal with correlated variabl... |

17 |
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(Show Context)
Citation Context ... for good introductions. Interesting machine learning applications include reinforcement learning [17], incorporation of derivative observations [18], speeding up the evaluation of Bayesian integrals =-=[19,20]-=-, and as models of dynamical systems [21]. The key assumption is that the posterior distribution p(y|x, D) is Gaussian. To compute its mean and variance, one specifies a valid covariance function cov(... |

7 | Bayesian Gaussian Processes for Classification and Regression - Gibbs - 1997 |

5 | Gaussian Processes for Regression and Optimisation
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(Show Context)
Citation Context ... for good introductions. Interesting machine learning applications include reinforcement learning [17], incorporation of derivative observations [18], speeding up the evaluation of Bayesian integrals =-=[19,20]-=-, and as models of dynamical systems [21]. The key assumption is that the posterior distribution p(y|x, D) is Gaussian. To compute its mean and variance, one specifies a valid covariance function cov(... |