Predictive Entropy Search for Multi-objective Bayesian Optimization

We present \small PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. \small PESMO chooses the evaluation points to maximally reduce the entropy of the posterior distribution over the Pareto set. The \small PESMO acquisition function is decomposed as a sum of objective-specific acquisition functions, which makes it possible to use the algorithm in \emphdecoupled scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability is useful to identify difficult objectives that require more evaluations. \small 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 \small PESMO with other methods on synthetic and real-world problems. The results show that \small PESMO produces better recommendations with a smaller number of evaluations, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.

Authors

• Daniel Hernández-Lobato
• José Miguel Hernández-Lobato
• Amar Shah 0001
• Ryan P. Adams

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