  We present PESMO, a Bayesian method for identifying the Pareto set of
multi-objective optimization problems, when the functions are expensive to
evaluate. The central idea of PESMO is to choose evaluation points so as to
maximally reduce the entropy of the posterior distribution over the Pareto set.
Critically, the PESMO multi-objective acquisition function can be decomposed as
a sum of objective-specific acquisition functions, which enables the algorithm
to be used in \emph{decoupled} scenarios in which the objectives can be
evaluated separately and perhaps with different costs. This decoupling
capability also makes it possible to identify difficult objectives that require
more evaluations. PESMO also offers gains in efficiency, as its cost scales
linearly with the number of objectives, in comparison to the exponential cost
of other methods. We compare PESMO with other related methods for
multi-objective Bayesian optimization on synthetic and real-world problems. The
results show that PESMO produces better recommendations with a smaller number
of evaluations of the objectives, and that a decoupled evaluation can lead to
improvements in performance, particularly when the number of objectives is
large.
