Black-box optimization of expensive functions using Bayesian optimization with a novel batch acquisition algorithm

  1. C. Domínguez Bravo
  2. J. Lozano
Actas:
1st Spanish Young Statisticians and Operational Researchers Meeting

Editorial: Universidad de Granada

Año de publicación: 2017

Páginas: 36

Tipo: Aportación congreso

Resumen

The problem of optimizing black-box expensive functions appears in many practical situations. Bayesianoptimization methodology has been successfully applied to solve them using Gaussian processes as surrogate models.Following this method, the original minimization problem is transformed into an iterative adaptive processwhere the points to be observed with the black-boxfunction are obtained by maximizing an auxiliary function called acquisition function. Of course, this auxiliary optimization problem can be solved easily applying standard techniques.Different single–point acquisition functions appear inthe literature considering a different trade-off betweenexploration (select points with high uncertainty) andexploitation (select points with high expected value).Nowadays, the technology development allows in somecases to perform evaluations of the expensive function in parallel at the same cost as a single evaluation.Therefore, there is a need of developing batch acquisition criteria to take advantage of this parallelism.In this presentation we will introduce a novel batchacquisition algorithm which selects the batch of pointsin two separated steps. Firstly, the Pareto–optimalset of the bi– objective problem defined by maximizingthe variance and minimizing the mean of the modelis approximated by means of an evolutionary multiobjective algorithm. Then, the batch is extracted fromthe approximated Pareto set as the set of points thatmaximize the mutual information with respect to theblack–box function. Some variants of the algorithmwill be also presented.We compare our strategies with state-of-the-art approaches in benchmark functions, obtaining betterresults. For a brief bibliography on the topic see:[1, 2, 3, 4]