High-dimensional Bayesian Optimization with Group Testing
Erik Orm Hellsten Carl Hvarfner Leonard Papenmeier Luigi Nardi
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.