Abstract
The acquisition function is the mechanism to implement the trade-off between exploration and exploitation in BO. More precisely, any acquisition function aims to guide the search of the optimum towards points with potential low values of objective function either because the prediction of \(f\left( x \right)\), based on the probabilistic surrogate model, is low or the uncertainty, also based on the same model, is high (or both).
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References
Astudillo, R., Frazier, P.: Bayesian optimization of composite functions. In: International Conference on Machine Learning, pp. 354–363 (2019, May)
Auer, P.: Using confidence bounds for exploitation-exploration trade-offs. J. Mach. Learn. Res. 3(3), 397–422 (2002)
Basu, K., Ghosh, S.: Analysis of Thompson sampling for Gaussian process optimization in the bandit setting (2017). arXiv preprint arXiv:1705.06808
Berger, J.O.: Statistical Decision Theory and Bayesian Analysis. Springer Science & Business Media (2013)
Brochu, E., Cora, V.M., de Freitas, N.: A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning (2010). arXiv preprint arXiv:1012.2599
Frazier, P., Powell, W., Dayanik, S.: The knowledge-gradient policy for correlated normal beliefs. Informs J. Comput. 21(4), 599–613 (2009)
Glasserman, P.: Performance continuity and differentiability in Monte Carlo optimization. In: 1988 Winter Simulation Conference Proceedings, pp. 518–524. IEEE (1988)
González, J., Osborne, M., Lawrence, N.D.: GLASSES: Relieving the Myopia of Bayesian Optimisation (2016)
Hennig, P., Schuler, C.J.: Entropy search for information-efficient global optimization. J. Mach. Learn. Res. 13, 1809–1837 (2012)
Hernández-Lobato, J.M., Hoffman, M.W., Ghahramani, Z.: Predictive entropy search for efficient global optimization of black-box functions. Adv. Neural. Inf. Process. Syst. 25, 144–149 (2014). https://doi.org/10.1016/j.molstruc.2009.06.011
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)
Kingma, D.P., Welling, M.: Auto-encoding variational bayes (2013). arXiv preprint arXiv:1312.6114
Krause, A., Golovin, D.:. Submodular function maximization. In: Tractability: practical Approaches to Hard Problems, pp. 71–104. Cambridge University Press (2014)
Kushner, H.J.: A new method of locating the maximum point of an arbitrary multi-peak curve in the presence of noise. J. Basic Eng. 86, 97–106 (1964)
Lam, R., Willcox, K., Wolpert, D.H.: Bayesian optimization with a finite budget: an approximate dynamic programming approach. Adv. Neural. Inf. Process. Syst. 30, 883–891 (2016). https://doi.org/10.1186/1471-2407-4-76
Marchant, R., Ramos, F., Sanner, S.: Sequential Bayesian optimisation for spatial-temporal monitoring. In: International Conference on Uncertainty in Artificial Intelligence, pp. 553–562 (2014)
Mockus, J., Tiesis, V., and Zilinskas, A.: The application of Bayesian methods for seeking the extremum. In: Dixon, L., Szego, G. (eds.) Towards Global Optimisation, 2, pp. 117–130. Elsevier (1978)
Nguyen, V., Osborne, M.A.: Knowing the what but not the where in Bayesian optimization (2019). arXiv preprint arXiv:1905.02685
Noè, U., Husmeier, D.: On a new improvement-based acquisition function for Bayesian optimization (2018). arXiv preprint arXiv:1808.06918
Osborne, M.A., Garnett, R., Roberts, S.J.: Gaussian processes for global optimization. In: 3rd International Conference on Learning and Intelligent Optimization (LION3), vol. 2009 (2009)
Poloczek, M., Wang, J., Frazier, P.: Multi-information source optimization.In: Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., Garnett, R. (eds.) Advances in Neural Information Processing Systems, 30, pp. 4291–4301. Curran Associates, Red Hook, NY (2017)
Russo, D., Van Roy, B., Kazerouni, A., Osband, I., Wen, Z.: A tutorial on Thompson sam-pling. Found. Trends Mach. Learn. 11, 1–96 (2018). https://doi.org/10.1561/2200000070
Srinivas, N., Krause, A., Kakade, S.M., Seeger, M.W.: Information-theoretic regret bounds for Gaussian process optimization in the bandit setting. In: IEEE Transactions on Information Theory, pp. 3250–3265 (2012)
Toscano-Palmerin, S., Frazier, P.I.: Bayesian optimization with expensive integrands (2018). arXiv preprint arXiv:1803.08661
Villemonteix, J., Vazquez, E., Walter, E.: An informational approach to the global optimization of expensive-to-evaluate functions. J. Global Optim. 44(4), 509 (2009)
Volpp, M., Fröhlich, L., Doerr, A., Hutter, F., Daniel, C.: Meta-learning acquisition functions for Bayesian optimization (2019). arXiv preprint arXiv:1904.02642
Wang, Z., Jegelka, S.: Max-value entropy search for efficient Bayesian optimization. In: Proceedings of the 34th International Conference on Machine Learning. Sydney, Australia (2017)
Wilson, J., Hutter, F., Deisenroth, M.: Maximizing acquisition functions for Bayesian optimization. In: Advances in Neural Information Processing Systems, pp. 9906–9917 (2018)
Wu, J., Frazier, P.: The parallel knowledge gradient method for batch bayesian optimization. In: Advances in Neural Information Processing Systems, pp. 3126–3134 (2016)
Wu, J., Frazier, P.I.: Discretization-free knowledge gradient methods for bayesian optimization (2017). arXiv preprint arXiv:1707.06541
Wu, J., Poloczek, M., Wilson, A.G., Frazier, P.: Bayesian optimization with gradients. In: Advances in Neural Information Processing Systems, pp. 5273–5284, (4.2.5) (2017)
Yan, L., Duan, X., Liu, B., Xu, J.: Bayesian optimization based on K-optimality. Entropy 20(8), 594 (2018)
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Archetti, F., Candelieri, A. (2019). The Acquisition Function. In: Bayesian Optimization and Data Science . SpringerBriefs in Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-24494-1_4
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