Joint Entropy Search for Multi-objective Bayesian Optimization
This work addresses multi-objective optimization problems for applications with competing objectives and limited evaluations, presenting an incremental improvement in acquisition functions.
The paper tackles the problem of multi-objective optimization with limited noisy evaluations by proposing Joint Entropy Search (JES), a novel information-theoretic acquisition function for Bayesian optimization, and demonstrates its effectiveness on synthetic and real-world problems using hypervolume metrics.
Many real-world problems can be phrased as a multi-objective optimization problem, where the goal is to identify the best set of compromises between the competing objectives. Multi-objective Bayesian optimization (BO) is a sample efficient strategy that can be deployed to solve these vector-valued optimization problems where access is limited to a number of noisy objective function evaluations. In this paper, we propose a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and outputs. We present several analytical approximations to the JES acquisition function and also introduce an extension to the batch setting. We showcase the effectiveness of this new approach on a range of synthetic and real-world problems in terms of the hypervolume and its weighted variants.