Bayesian Optimization (BO) methods are useful for optimizing functions that
are expen- sive to evaluate, lack an analytical expression and whose
evaluations can be contaminated by noise. These methods rely on a probabilistic
model of the objective function, typically a Gaussian process (GP), upon which
an acquisition function is built. The acquisition function guides the
optimization process and measures the expected utility of performing an
evaluation of the objective at a new point. GPs assume continous input
variables. When this is not the case, for example when some of the input
variables take categorical or integer values, one has to introduce extra
approximations. Consider a suggested input location taking values in the real
line. Before doing the evaluation of the objective, a common approach is to use
a one hot encoding approximation for categorical variables, or to round to the
closest integer, in the case of integer-valued variables. We show that this can
lead to problems in the optimization process and describe a more principled
approach to account for input variables that are categorical or integer-valued.
We illustrate in both synthetic and a real experiments the utility of our
approach, which significantly improves the results of standard BO methods using
Gaussian processes on problems with categorical or integer-valued variables.

该研究提出了更准确处理分类变量和整数值变量的方法，以改进使用高斯过程的贝叶斯优化方法在这些问题上的结果表现。