An Entropy Search Portfolio for Bayesian Optimization

TL;DR

The paper introduces the Entropy Search Portfolio (ESP), a novel Bayesian optimization approach that intelligently combines acquisition functions based on information theory, outperforming existing methods and demonstrating robustness across various problems.

Contribution

The paper proposes the Entropy Search Portfolio (ESP), a new information-theoretic method for combining acquisition functions in Bayesian optimization, improving performance and robustness.

Findings

ESP outperforms existing portfolio methods on real and synthetic problems.

ESP often surpasses the best individual acquisition function.

ESP is robust to poor acquisition functions inclusion.

Abstract

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misleading. To address this issue, we introduce the Entropy Search Portfolio (ESP): a novel approach to portfolio construction which is motivated by information theoretic considerations. We show that ESP outperforms existing portfolio methods on several real and synthetic problems, including geostatistical datasets and simulated control tasks. We not only show that ESP is able to offer performance as good as the best, but unknown, acquisition function, but surprisingly it often gives better performance. Finally, over a wide range of conditions we find that ESP is robust to the inclusion of poor acquisition functions.