Joint Entropy Search for Maximally-Informed Bayesian Optimization
This provides a new go-to acquisition function for Bayesian optimization, addressing the need for efficient and effective decision-making in optimization problems, though it appears incremental as it builds on existing information-theoretic methods.
The paper tackled the problem of optimizing expensive-to-evaluate black-box functions by proposing Joint Entropy Search (JES), a novel information-theoretic acquisition function that considers the entropy over the joint optimal probability density in both input and output space, resulting in state-of-the-art performance across a wide suite of tasks with minimal computational overhead.
Information-theoretic Bayesian optimization techniques have become popular for optimizing expensive-to-evaluate black-box functions due to their non-myopic qualities. Entropy Search and Predictive Entropy Search both consider the entropy over the optimum in the input space, while the recent Max-value Entropy Search considers the entropy over the optimal value in the output space. We propose Joint Entropy Search (JES), a novel information-theoretic acquisition function that considers an entirely new quantity, namely the entropy over the joint optimal probability density over both input and output space. To incorporate this information, we consider the reduction in entropy from conditioning on fantasized optimal input/output pairs. The resulting approach primarily relies on standard GP machinery and removes complex approximations typically associated with information-theoretic methods. With minimal computational overhead, JES shows superior decision-making, and yields state-of-the-art performance for information-theoretic approaches across a wide suite of tasks. As a light-weight approach with superior results, JES provides a new go-to acquisition function for Bayesian optimization.