Predictive Entropy Search for Multi-objective Bayesian Optimization

We present MPES, a method for multi-objective Bayesian optimization of expensive-to-evaluate black-box functions. At each iteration, MPES chooses an input location to evaluate each objective function on so as to maximally reduce the entropy of the Pareto set of the associated optimization task. The acquisition function employed by MPES is expressed as a sum over the objectives. This enables its use in a \emph{decoupled} scenario, where the different objectives may be evaluated at different input locations in each iteration. Experiments comparing MPES with other related methods from the literature show that it produces significantly better recommendations with a smaller number of evaluations of the objective functions.