Global Optimization with Gaussian Regression Under the Finite Number of Evaluation

Naoya Takimoto, Hiroshi Morita

Abstract

Computer experiments are black-box functions that are expensive to evaluate. One solution to expensive black-box optimization is Bayesian optimization with Gaussian processes. This approach is popularly used in this challenge, and it is efficient when the number of evaluations is limited by cost and time constraints, which is generally true in practice. This paper discusses an optimization method with two acquisition functions. Our new method improves the efficiency of global optimization when the number of evaluations is strictly limited.

References

  1. Brochu, E., Cora, V. M., and De Freitas, N. (2010). A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599.
  2. Hoffman, M. D., Brochu, E., and de Freitas, N. (2011). Portfolio allocation for Bayesian optimization. In UAI, pages 327-336. Citeseer.
  3. Jones, D. R., Schonlau, M., and Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. J. of Global Optimization, 13(4):455-492.
  4. Kushner, H. J. (1964). A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Fluids Engineering, 86(1):97-106.
  5. Martin, J. D. and Simpson, T. W. (2003). A study on the use of kriging models to approximate deterministic computer models. In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pages 567-576. American Society of Mechanical Engineers.
  6. Mockus, J. (1994). Application of bayesian approach to numerical methods of global and stochastic optimization. Journal of Global Optimization, 4(4):347-365.
  7. Mockus, J., Tiesis, V., and Zilinskas, A. (1978). The application of bayesian methods for seeking the extremum. Towards Global Optimization, 2(117-129):2.
  8. Santner, T. J., Williams, B. J., and Notz, W. (2003). The design and analysis of computer experiments. Springer Science & Business Media.
  9. Sasena, M. J. (2002). Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. PhD thesis, General Motors.
  10. Zoua, D., Wangb, X., and Duana, N. (2014). An improved particle swarm optimization algorithm for chaotic synchronization based on pid control. Journal of Information & Computational Science, 11(9):3177- 3186.
Download


Paper Citation


in Harvard Style

Takimoto N. and Morita H. (2015). Global Optimization with Gaussian Regression Under the Finite Number of Evaluation . In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-120-5, pages 192-198. DOI: 10.5220/0005559701920198


in Bibtex Style

@conference{simultech15,
author={Naoya Takimoto and Hiroshi Morita},
title={Global Optimization with Gaussian Regression Under the Finite Number of Evaluation},
booktitle={Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2015},
pages={192-198},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005559701920198},
isbn={978-989-758-120-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Global Optimization with Gaussian Regression Under the Finite Number of Evaluation
SN - 978-989-758-120-5
AU - Takimoto N.
AU - Morita H.
PY - 2015
SP - 192
EP - 198
DO - 10.5220/0005559701920198