arXiv subjects

Masayuki Karasuyama

Publications and source records attributed to Masayuki Karasuyama.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Information-Theoretic Approach to Constrained Multi-Fidelity Multi-Objective Bayesian Optimization

Bayesian optimization often involves multiple objectives, constraints, and fidelity levels. We address the challenge of jointly selecting where and at which fidelity to evaluate to identify the highest-fidelity feasible Pareto frontier in this combined setting. From a unified information-theoretic perspective, we measure query utility by the information gain about this frontier, provided by an observation. Since this mutual information is intractable, we derive a variational lower bound using a mixture of under- and over-truncated approximations to the Pareto-consistent region. Multi-fidelity surrogate models propagate the information to arbitrary fidelities, yielding a cost-aware acquisition function without separate heuristics for fidelity selection or constraint handling. Experiments on synthetic, benchmark, and real-world problems demonstrate effectiveness across diverse objective, constraint, and fidelity settings.

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arXiv2026

Pre-training of Bayesian Optimization Algorithm through Bayesian Optimization

Bayesian optimization (BO) is widely used as a standard approach for expensive black-box optimization. However, BO algorithms often involve parameters that must be specified in advance, and their performance can strongly depend on these choices. We propose a framework for optimizing such parameters using sample paths drawn from a Gaussian process (GP) inferred from the information available at the start of BO. We use cumulative regret as the performance metric for a BO algorithm. By running the BO algorithm on the generated sample paths, we obtain an empirical estimate of its expected cumulative regret for a given parameter configuration. Optimizing this estimate allows us to identify parameter configurations that, given the currently available information, are expected to achieve low cumulative regret. Since this parameter optimization is itself a black-box optimization problem, we employ another BO procedure to solve it, which we refer to as outer BO. Through experiments, we demonstrate that the proposed framework can effectively select parameter configurations that achieve strong performance among a range of candidate configurations.

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arXiv2026

Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems

A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers Bayesian optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.

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arXiv2026

Exact Subgraph Isomorphism Network with Mixed $L_{0,2}$ Norm Constraint for Predictive Graph Mining

In the graph-level prediction task (predict a label for a given graph), the information contained in subgraphs of the input graph plays a key role. In this paper, we propose Exact subgraph Isomorphism Network (EIN), which combines the exact subgraph enumeration, a neural network, and a sparse regularization by the mixed $L_{0,2}$ norm constraint. In general, building a graph-level prediction model achieving high discriminative ability along with interpretability is still a challenging problem. Our combination of the subgraph enumeration and neural network contributes to high discriminative ability about the subgraph structure of the input graph. Further, the sparse regularization in EIN enables us 1) to derive an effective pruning strategy that mitigates computational difficulty of the enumeration while maintaining the prediction performance, and 2) to identify important subgraphs that contributes to high interpretability. We empirically show that EIN has sufficiently high prediction performance compared with standard graph neural network models, and also, we show examples of post-hoc analysis based on the selected subgraphs.

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arXiv2025

Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization

Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments.

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arXiv2025

Pareto-frontier Entropy Search with Variational Lower Bound Maximization

This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which is defined as a distribution truncated by the Pareto-frontier. However, it is usually impossible to obtain the entire Pareto-frontier in a continuous domain, and therefore, the complete truncation cannot be known. We consider an approximation of the truncate distribution by using a mixture distribution consisting of two possible approximate truncation obtainable from a subset of the Pareto-frontier, which we call over- and under-truncation. Since the optimal balance of the mixture is unknown beforehand, we propose optimizing the balancing coefficient through the variational lower bound maximization framework, by which the approximation error of the information gain can be minimized. Our empirical evaluation demonstrates the effectiveness of the proposed method particularly when the number of objective functions is large.

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arXiv2025

Active learning for level set estimation under input uncertainty and its extensions

Testing under what conditions the 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 so far, there are still many issues to be solved for their practical usage. As one of such issues, we consider the case where the input conditions cannot be controlled precisely, i.e., LSE problems under input uncertainty. We introduce a basic framework for handling input uncertainty in LSE problem, 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 the applicability and effectiveness.

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arXiv2025

Regret Analysis for Randomized Gaussian Process Upper Confidence Bound

Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows a GP. One notable drawback of GP-UCB is that the theoretical confidence parameter $β$ increases along with the iterations and is too large. To alleviate this drawback, this paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB (IRGP-UCB), which uses the confidence parameter generated from the shifted exponential distribution. We analyze the expected regret and conditional expected regret, where the expectation and the probability are taken respectively with $f$ and noise and with the randomness of the BO algorithm. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite. Furthermore, we show that randomization plays a key role in avoiding an increase in confidence parameter by showing that GP-UCB using a constant confidence parameter can incur linearly growing expected cumulative regret. Finally, we show numerical experiments using synthetic and benchmark functions and real-world emulators.

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arXiv2025

Bayesian Optimization for Simultaneous Selection of Machine Learning Algorithms and Hyperparameters on Shared Latent Space

Selecting the optimal combination of a machine learning (ML) algorithm and its hyper-parameters is crucial for the development of high-performance ML systems. However, since the combination of ML algorithms and hyper-parameters is enormous, the exhaustive validation requires a significant amount of time. Many existing studies use Bayesian optimization (BO) for accelerating the search. On the other hand, a significant difficulty is that, in general, there exists a different hyper-parameter space for each one of candidate ML algorithms. BO-based approaches typically build a surrogate model independently for each hyper-parameter space, by which sufficient observations are required for all candidate ML algorithms. In this study, our proposed method embeds different hyper-parameter spaces into a shared latent space, in which a surrogate multi-task model for BO is estimated. This approach can share information of observations from different ML algorithms by which efficient optimization is expected with a smaller number of total observations. We further propose the pre-training of the latent space embedding with an adversarial regularization, and a ranking model for selecting an effective pre-trained embedding for a given target dataset. Our empirical study demonstrates effectiveness of the proposed method through datasets from OpenML.

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arXiv2024

Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

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arXiv2024

Learning Attributed Graphlets: Predictive Graph Mining by Graphlets with Trainable Attribute

The graph classification problem has been widely studied; however, achieving an interpretable model with high predictive performance remains a challenging issue. This paper proposes an interpretable classification algorithm for attributed graph data, called LAGRA (Learning Attributed GRAphlets). LAGRA learns importance weights for small attributed subgraphs, called attributed graphlets (AGs), while simultaneously optimizing their attribute vectors. This enables us to obtain a combination of subgraph structures and their attribute vectors that strongly contribute to discriminating different classes. A significant characteristics of LAGRA is that all the subgraph structures in the training dataset can be considered as a candidate structures of AGs. This approach can explore all the potentially important subgraphs exhaustively, but obviously, a naive implementation can require a large amount of computations. To mitigate this issue, we propose an efficient pruning strategy by combining the proximal gradient descent and a graph mining tree search. Our pruning strategy can ensure that the quality of the solution is maintained compared to the result without pruning. We empirically demonstrate that LAGRA has superior or comparable prediction performance to the standard existing algorithms including graph neural networks, while using only a small number of AGs in an interpretable manner.

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arXiv2023

Multi-Objective Bayesian Optimization with Active Preference Learning

There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective functions and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.

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arXiv2023

Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $β$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $β$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

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arXiv2023

Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

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arXiv2023

Bayesian Optimization for Cascade-type Multi-stage Processes

Complex processes in science and engineering are often formulated as multistage decision-making problems. In this paper, we consider a type of multistage decision-making process called a cascade process. A cascade process 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 an extension called suspension setting 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, which was the motivation for this study.

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arXiv2022

Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound

Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.

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arXiv2022

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.

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arXiv2021

Distance Metric Learning for Graph Structured Data

Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between input graphs, defining an appropriate distance metric for graphs remains a controversial issue. Hence, we propose a supervised distance metric learning method for the graph classification problem. Our method, named interpretable graph metric learning (IGML), learns discriminative metrics in a subgraph-based feature space, which has a strong graph representation capability. By introducing a sparsity-inducing penalty on the weight of each subgraph, IGML can identify a small number of important subgraphs that can provide insight into the given classification task. Because our formulation has a large number of optimization variables, an efficient algorithm that uses pruning techniques based on safe screening and working set selection methods is also proposed. An important property of IGML is that solution optimality is guaranteed because the problem is formulated as a convex problem and our pruning strategies only discard unnecessary subgraphs. Furthermore, we show that IGML is also applicable to other structured data such as itemset and sequence data, and that it can incorporate vertex-label similarity by using a transportation-based subgraph feature. We empirically evaluate the computational efficiency and classification performance of IGML on several benchmark datasets and provide some illustrative examples of how IGML identifies important subgraphs from a given graph dataset.

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