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The Correlated Knowledge Gradient for Simulation Optimization of Continuous Parameters using Gaussian Process Regression
Abstract
We extend the concept of the correlated knowledge-gradient policy for the ranking and selection of a finite set of alternatives to the case of continuous decision variables. We propose an approximate knowledge gradient for problems with continuous decision variables in the context of a Gaussian process regression model in a Bayesian setting, along with an algorithm to maximize the approximate knowledge gradient. In the problem class considered, we use the knowledge gradient for continuous parameters to sequentially choose where to sample an expensive noisy function in order to find the maximum quickly. We show that the knowledge gradient for continuous decisions is a generalization of the efficient global optimization algorithm proposed in [D. R. Jones, M. Schonlau and W. J. Welch, J. Global Optim., 13 (1998), pp. 455–492].
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Cites
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
A Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
Efficient Global Optimization of Expensive Black-Box Functions
Jones, D. R., Schonlau, M., & Welch, W. J. (1998) · Journal of Global Optimization · doi:10.1023/a:1008306431147 · Cited by 8,070
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Lookman, T., Balachandran, P. V., Xue, D., & Yuan, R. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0153-8 · Cited by 832
Recent Advances in Bayesian Optimization
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Tuo, R., & Wang, W. (2020) · arXiv · doi:10.48550/arxiv.2002.01569 · Cited by 2
Metadata
- Authors
- Scott, W., Frazier, P., & Powell, W.
- Venue
- SIAM Journal on Optimization
- Published
- 2011-07
- Volume
- 21
- Issue
- 3
- Pages
- 996-1026
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2004808074
- Cited by
- 209
- References
- 3
- FWCI
- 6.07
- Type
- journal article
- Language
- en
- Open access
- closed
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