Multi-Objective Batch Energy-Entropy Acquisition Function for Bayesian Optimization

Bayesian Optimization (BO) provides an efficient framework for optimizing expensive black-box functions by employing a surrogate model (typically a Gaussian Process) to approximate the objective function and an acquisition function to guide the search for optimal points. Batch BO extends this paradigm by selecting and evaluating multiple candidate points simultaneously, which improves computational efficiency but introduces challenges in optimizing the resulting high-dimensional acquisition functions. Among existing acquisition functions for batch Bayesian Optimization, entropy-based methods are considered to be state-of-the-art methods due to their ability to enable more globally efficient while avoiding redundant evaluations. However, they often fail to fully capture the dependencies and interactions among the selected batch points. In this work, we propose a Multi-Objective Batch Energy–Entropy acquisition function for Bayesian Optimization (MOBEEBO), which adaptively exploits the correlations among batch points. In addition, MOBEEBO incorporates multiple types of acquisition functions as objectives in a unified framework to achieve more effective batch diversity and quality. Empirical results demonstrate that the proposed algorithm is applicable to a wide range of optimization problems and achieves competitive performance.