Differentiating the Multipoint Expected Improvement for Optimal Batch Design

Marmin, Sébastien Guillaume; Chevalier, Clément; Ginsbourger, David (2015). Differentiating the Multipoint Expected Improvement for Optimal Batch Design. In: Pardalos, Panos; Pavone, Mario; Farinella, Giovanni Maria; Cutello, Vincenzo (eds.) Machine Learning, Optimization, and Big Data. Lecture Notes in Computer Science: Vol. 9432 (pp. 37-48). Cham: Springer 10.1007/978-3-319-27926-8_4

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This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.

Item Type:

Book Section (Book Chapter)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Marmin, Sébastien Guillaume; Chevalier, Clément and Ginsbourger, David


300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics




Lecture Notes in Computer Science






Lutz Dümbgen

Date Deposited:

07 Apr 2016 11:00

Last Modified:

07 Apr 2016 11:00

Publisher DOI:






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