  Bayesian optimization involves "inner optimization" over a new-data
acquisition criterion which is non-convex/highly multi-modal, may be
non-differentiable, or may otherwise thwart local numerical optimizers. In such
cases it is common to replace continuous search with a discrete one over random
candidates. Here we propose using candidates based on a Delaunay triangulation
of the existing input design. We detail the construction of these "tricands"
and demonstrate empirically how they outperform both numerically optimized
acquisitions and random candidate-based alternatives, and are well-suited for
hybrid schemes, on benchmark synthetic and real simulation experiments.
