R1: We do agree that our approach is complex and involves "multiple approximation steps". C2: On Park1, the NN "finds the global optimum after one query point"-- How is this significant... " First, the quality of the query point very much depends on the accuracy of the surrogate model. C3: Details about hyper-parameter selection; no liberty to choose a heldout dataset in practice. We optimized the hyper-parameters to minimize the average test error. We will supplement these details.

Multi-fidelity Bayesian optimization (MFBO) leverages experimental and/or computational data of varying quality and resource cost to optimize towards desired maxima cost-effectively. This approach is particularly attractive for chemical discovery due to MFBO's ability to integrate diverse data sources. Here, we investigate the application of MFBO to accelerate the identification of promising molecules or materials. We specifically analyze the conditions under which lower-fidelity data can enhance performance compared to single-fidelity problem formulations. We address two key challenges: selecting the optimal acquisition function, understanding the impact of cost, and data fidelity correlation. We then discuss how to assess the effectiveness of MFBO for chemical discovery.

In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. For example, the designer may need to tune the hyperparameters of neural network models for different learning tasks over time. Rather than evaluating the objective function for each candidate solution, the designer may have access to approximations of the objective functions, for which higher-fidelity evaluations entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information accrued about the optimal value or solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method includes shared inter-task latent variables, which are transferred across tasks by implementing particle-based variational Bayesian updates. Experimental results across synthetic and real-world examples reveal that the proposed provident acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.

Bayesian optimization (BO) is an effective tool for black-box optimization in which objective function evaluation is usually quite expensive. In practice, lower fidelity approximations of the objective function are often available. Recently, multi-fidelity Bayesian optimization (MFBO) has attracted considerable attention because it can dramatically accelerate the optimization process by using those cheaper observations. We propose a novel information theoretic approach to MFBO. Information-based approaches are popular and empirically successful in BO, but existing studies for information-based MFBO are plagued by difficulty for accurately estimating the information gain. Our approach is based on a variant of information-based BO called max-value entropy search (MES), which greatly facilitates evaluation of the information gain in MFBO. In fact, computations of our acquisition function is written analytically except for one dimensional integral and sampling, which can be calculated efficiently and accurately. We demonstrate effectiveness of our approach by using synthetic and benchmark datasets, and further we show a real-world application to materials science data.