Complex processes in science and engineering are often formulated as multistage decision-making problems. In this letter, we consider a cascade process, a type of multistage decision-making process. This is a multistage process in which the output of one stage is used as an input for the subsequent stage. When the cost of each stage is expensive, it is difficult to search for the optimal controllable parameters for each stage exhaustively. To address this problem, we formulate the optimization of the cascade process as an extension of the Bayesian optimization framework and propose two types of acquisition functions based on credible intervals and expected improvement. We investigate the theoretical properties of the proposed acquisition functions and demonstrate their effectiveness through numerical experiments. In addition, we consider suspension setting, an extension in which we are allowed to suspend the cascade process at the middle of the multistage decision-making process that often arises in practical problems. We apply the proposed method in a test problem involving a solar cell simulator, the motivation for this study.

Bayesian optimization (BO) is a popular method for expensive black-box optimization problems; however, querying the objective function at every iteration can be a bottleneck that hinders efficient search capabilities. In this regard, multifidelity Bayesian optimization (MFBO) aims to accelerate BO by incorporating lower-fidelity observations available with a lower sampling cost. In our previous work, we proposed an information-theoretic approach to MFBO, referred to as multifidelity max-value entropy search (MF-MES), which inherits practical effectiveness and computational simplicity of the well-known max-value entropy search (MES) for the single-fidelity BO. However, the applicability of MF-MES is still limited to the case that a single observation is sequentially obtained. In this letter, we generalize MF-MES so that information gain can be evaluated even when multiple observations are simultaneously obtained. This generalization enables MF-MES to address two practical problem settings: synchronous parallelization and trace-aware querying. We show that the acquisition functions for these extensions inherit the simplicity of MF-MES without introducing additional assumptions. We also provide computational techniques for entropy evaluation and posterior sampling in the acquisition functions, which can be commonly used for all variants of MF-MES. The effectiveness of MF-MES is demonstrated using benchmark functions and real-world applications such as materials science data and hyperparameter tuning of machine-learning algorithms.

Testing under what conditions a product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function, this task can be interpreted as the problem called level set estimation (LSE): the problem of identifying input regions such that the function value is above (or below) a threshold. Although various methods for LSE problems have been developed, many issues remain to be solved for their practical use. As one of such issues, we consider the case where the input conditions cannot be controlled precisely—LSE problems under input uncertainty. We introduce a basic framework for handling input uncertainty in LSE problems and then propose efficient methods with proper theoretical guarantees. The proposed methods and theories can be generally applied to a variety of challenges related to LSE under input uncertainty such as cost-dependent input uncertainties and unknown input uncertainties. We apply the proposed methods to artificial and real data to demonstrate their applicability and effectiveness.

In this letter, we study an active learning problem for maximizing an unknown linear function with high-dimensional binary features. This problem is notoriously complex but arises in many important contexts. When the sampling budget, that is, the number of possible function evaluations, is smaller than the number of dimensions, it tends to be impossible to identify all of the optimal binary features. Therefore, in practice, only a small number of such features are considered, with the majority kept fixed at certain default values, which we call the working set heuristic . The main contribution of this letter is to formally study the working set heuristic and present a suite of theoretically robust algorithms for more efficient use of the sampling budget. Technically, we introduce a novel method for estimating the confidence regions of model parameters that is tailored to active learning with high-dimensional binary features. We provide a rigorous theoretical analysis of these algorithms and prove that a commonly used working set heuristic can identify optimal binary features with favorable sample complexity. We explore the performance of the proposed approach through numerical simulations and an application to a functional protein design problem.

Distance metric learning has been widely used to obtain the optimal distance function based on the given training data. We focus on a triplet-based loss function, which imposes a penalty such that a pair of instances in the same class is closer than a pair in different classes. However, the number of possible triplets can be quite large even for a small data set, and this considerably increases the computational cost for metric optimization. In this letter, we propose safe triplet screening that identifies triplets that can be safely removed from the optimization problem without losing the optimality. In comparison with existing safe screening studies, triplet screening is particularly significant because of the huge number of possible triplets and the semidefinite constraint in the optimization problem. We demonstrate and verify the effectiveness of our screening rules by using several benchmark data sets.