  This work presents PESMOC, Predictive Entropy Search for Multi-objective
Bayesian Optimization with Constraints, an information-based strategy for the
simultaneous optimization of multiple expensive-to-evaluate black-box functions
under the presence of several constraints. PESMOC can hence be used to solve a
wide range of optimization problems. Iteratively, PESMOC chooses an input
location on which to evaluate the objective functions and the constraints so as
to maximally reduce the entropy of the Pareto set of the corresponding
optimization problem. The constraints considered in PESMOC are assumed to have
similar properties to those of the objective functions in typical Bayesian
optimization problems. That is, they do not have a known expression (which
prevents gradient computation), their evaluation is considered to be very
expensive, and the resulting observations may be corrupted by noise. These
constraints arise in a plethora of expensive black-box optimization problems.
We carry out synthetic experiments to illustrate the effectiveness of PESMOC,
where we sample both the objectives and the constraints from a Gaussian process
prior. The results obtained show that PESMOC is able to provide better
recommendations with a smaller number of evaluations than a strategy based on
random search.
