International Workshop on Machine Learning, Optimization and Big Data

Machine Learning, Optimization, and Big Data pp 37-48

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

  • Sébastien Marmin
  • Clément Chevalier
  • David Ginsbourger
Conference paper

DOI: 10.1007/978-3-319-27926-8_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9432)
Cite this paper as:
Marmin S., Chevalier C., Ginsbourger D. (2015) Differentiating the Multipoint Expected Improvement for Optimal Batch Design. In: Pardalos P., Pavone M., Farinella G., Cutello V. (eds) Machine Learning, Optimization, and Big Data. Lecture Notes in Computer Science, vol 9432. Springer, Cham

Abstract

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 batch-sequential 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.

Keywords

Bayesian optimization Batch-sequential design GP UCB 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sébastien Marmin
    • 1
    • 2
    • 3
  • Clément Chevalier
    • 4
    • 5
  • David Ginsbourger
    • 1
    • 6
  1. 1.Department of Mathematics and Statistics, IMSVUniversity of BernBernSwitzerland
  2. 2.Institut de Radioprotection et de Sûreté NucléaireCadaracheFrance
  3. 3.École Centrale de MarseilleMarseilleFrance
  4. 4.Institute of StatisticsUniversity of NeuchâtelNeuchâtelSwitzerland
  5. 5.Institute of MathematicsUniversity of ZurichZürichSwitzerland
  6. 6.Idiap Research InstituteMartignySwitzerland

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