Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations

Eero Siivola, Aki Vehtari, Jarno Vanhatalo, Javier Gonzalez, Michael Andersen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of ℛ d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.
Original languageEnglish
Title of host publication2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)
EditorsN Pustelnik, Z Ma, ZH Tan, J Larsen
Number of pages6
Volume28
PublisherIEEE
Publication dateNov 2018
ISBN (Electronic)978-1-5386-5477-4
Publication statusPublished - Nov 2018
MoE publication typeA4 Article in conference proceedings
EventIEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING - Aalborg, Denmark
Duration: 17 Sep 201820 Sep 2018
Conference number: 28
http://mlsp2018.conwiz.dk/home.htm

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing
PublisherIEEE
ISSN (Print)2161-0363

Fields of Science

  • 112 Statistics and probability
  • 113 Computer and information sciences
  • Bayesian optimization
  • Gaussian process
  • virtual derivative sign observation

Cite this

Siivola, E., Vehtari, A., Vanhatalo, J., Gonzalez, J., & Andersen, M. (2018). Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations. In N. Pustelnik, Z. Ma, ZH. Tan, & J. Larsen (Eds.), 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP) (Vol. 28). (IEEE International Workshop on Machine Learning for Signal Processing). IEEE.
Siivola, Eero ; Vehtari, Aki ; Vanhatalo, Jarno ; Gonzalez, Javier ; Andersen, Michael. / Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations. 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP). editor / N Pustelnik ; Z Ma ; ZH Tan ; J Larsen. Vol. 28 IEEE, 2018. (IEEE International Workshop on Machine Learning for Signal Processing).
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title = "Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations",
abstract = "Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of ℛ d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.",
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Siivola, E, Vehtari, A, Vanhatalo, J, Gonzalez, J & Andersen, M 2018, Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations. in N Pustelnik, Z Ma, ZH Tan & J Larsen (eds), 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP). vol. 28, IEEE International Workshop on Machine Learning for Signal Processing, IEEE, IEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING, Aalborg, Denmark, 17/09/2018.

Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations. / Siivola, Eero; Vehtari, Aki; Vanhatalo, Jarno ; Gonzalez, Javier; Andersen, Michael.

2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP). ed. / N Pustelnik; Z Ma; ZH Tan; J Larsen. Vol. 28 IEEE, 2018. (IEEE International Workshop on Machine Learning for Signal Processing).

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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T1 - Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations

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AU - Vanhatalo, Jarno

AU - Gonzalez, Javier

AU - Andersen, Michael

PY - 2018/11

Y1 - 2018/11

N2 - Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of ℛ d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.

AB - Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of ℛ d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.

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M3 - Conference contribution

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Siivola E, Vehtari A, Vanhatalo J, Gonzalez J, Andersen M. Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations. In Pustelnik N, Ma Z, Tan ZH, Larsen J, editors, 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP). Vol. 28. IEEE. 2018. (IEEE International Workshop on Machine Learning for Signal Processing).