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Many real-world problems can be phrased as a multi-objective optimizationproblem, where the goal is to identify the best set of compromises between thecompeting objectives. Multi-objective Bayesian optimization (BO) is a sampleefficient strategy that can be deployed to solve these vector-valuedoptimization problems where access is limited to a number of noisy objectivefunction evaluations. In this paper, we propose a novel information-theoreticacquisition function for BO called Joint Entropy Search (JES), which considersthe joint information gain for the optimal set of inputs and outputs. Wepresent several analytical approximations to the JES acquisition function andalso introduce an extension to the batch setting. We showcase the effectivenessof this new approach on a range of synthetic and real-world problems in termsof the hypervolume and its weighted variants.

Joint Entropy Search for Multi-objective Bayesian Optimization