In this work, we have chosen to represent the parameters as continuous variables rather than evaluating the acquisition function on a predefined list of candidates. Some optimization packages preferentially treat search spaces as fully discrete whereas others preferentially treat search spaces as continuous. The Ax Platform is designed and configured in a way that favors optimization of continuous spaces. To optimize over a predefined list of candidates in the Ax Platform requires digging into lower level components in order to evaluate the acquisition function directly (see e.g., ). In addition to requiring more user expertise, evaluating quasi-random predefined candidates is typically less efficient than relying on internal maximization of the acquisition function. In cases where the problem is high-dimensional, the number of predefined points required to effectively sample the acquisition function may be prohibitive compared to the continuous case. This is not to suggest that evaluating acquisition functions over predefined points is undesirable, but rather that there are non-negligible implementation and computational costs associated with it. In the context of this work, this discussion applies to invariances that do not involve a change of variables (i.e., a linear equality constraint. See discussion in Appendix B.1).