Wang, Ziyu; Hutter, Frank; Zoghi, Masrour; Matheson, David; de Feitas, Nando Bayesian optimization in a billion dimensions via random embeddings. (English) Zbl 1358.90089 J. Artif. Intell. Res. (JAIR) 55, 361-387 (2016). Summary: Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting random embedding Bayesian optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver. Cited in 1 ReviewCited in 29 Documents MSC: 90C15 Stochastic programming 62C10 Bayesian problems; characterization of Bayes procedures Keywords:categorical variables; continuous variables; mixed integer linear programming solver Software:lpSolve PDFBibTeX XMLCite \textit{Z. Wang} et al., J. Artif. Intell. Res. (JAIR) 55, 361--387 (2016; Zbl 1358.90089) Full Text: DOI arXiv