High-dimensional Bayesian Optimization with Group Testing

TL;DR

This paper introduces GTBO, a novel Bayesian optimization method that uses group testing to identify active variables in high-dimensional black-box functions, improving efficiency and interpretability.

Contribution

The paper proposes a new group testing-based algorithm for high-dimensional Bayesian optimization that identifies active variables to enhance optimization efficiency.

Findings

GTBO effectively identifies active variables in high-dimensional spaces.

GTBO outperforms existing methods on synthetic and real-world tasks.

GTBO helps practitioners understand which parameters influence the objective.

Abstract

Bayesian optimization is an effective method for optimizing expensive-to-evaluate black-box functions. High-dimensional problems are particularly challenging as the surrogate model of the objective suffers from the curse of dimensionality, which makes accurate modeling difficult. We propose a group testing approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective. To that end, we extend the well-established theory of group testing to functions of continuous ranges. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By exploiting the axis-aligned subspace assumption, GTBO is competitive against state-of-the-art methods on several synthetic and real-world high-dimensional optimization tasks. Furthermore, GTBO aids in the discovery of active parameters in applications, thereby enhancing practitioners' understanding of the problem at hand.