High-dimensional Bayesian Optimization with Group Testing
This addresses the curse of dimensionality in Bayesian optimization for practitioners, though it is incremental as it builds on existing group testing theory.
The paper tackles the challenge of high-dimensional Bayesian optimization by proposing a group testing approach to identify active variables, resulting in competitive performance against state-of-the-art methods on synthetic and real-world tasks.
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.