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Shogo Iwazaki

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7 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Gaussian Process Upper Confidence Bound Achieves Nearly-Optimal Regret in Noise-Free Gaussian Process Bandits

Shogo Iwazaki

We study the noise-free Gaussian Process (GP) bandit problem, in which a learner seeks to minimize regret through noise-free observations of a black-box objective function that lies in a known reproducing kernel Hilbert space (RKHS). The Gaussian Process Upper Confidence Bound (GP-UCB) algorithm is a well-known approach for GP bandits, where query points are adaptively selected based on the GP-based upper confidence bound score. While several existing works have reported the practical success of GP-UCB, its theoretical performance remains suboptimal. However, GP-UCB often empirically outperforms other nearly-optimal noise-free algorithms that use non-adaptive sampling schemes. This paper resolves the gap between theoretical and empirical performance by establishing a nearly-optimal regret upper bound for noise-free GP-UCB. Specifically, our analysis provides the first constant cumulative regret bounds in the noise-free setting for both the squared exponential kernel and the Matérn kernel with some degree of smoothness.

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ICML Conference 2025 Conference Paper

Improved Regret Analysis in Gaussian Process Bandits: Optimality for Noiseless Reward, RKHS norm, and Non-Stationary Variance

Shogo Iwazaki
Shion Takeno

We study the Gaussian process (GP) bandit problem, whose goal is to minimize regret under an unknown reward function lying in some reproducing kernel Hilbert space (RKHS). The maximum posterior variance analysis is vital in analyzing near-optimal GP bandit algorithms such as maximum variance reduction (MVR) and phased elimination (PE). Therefore, we first show the new upper bound of the maximum posterior variance, which improves the dependence of the noise variance parameters of the GP. By leveraging this result, we refine the MVR and PE to obtain (i) a nearly optimal regret upper bound in the noiseless setting and (ii) regret upper bounds that are optimal with respect to the RKHS norm of the reward function. Furthermore, as another application of our proposed bound, we analyze the GP bandit under the time-varying noise variance setting, which is the kernelized extension of the linear bandit with heteroscedastic noise. For this problem, we show that MVR and PE-based algorithms achieve noise variance-dependent regret upper bounds, which matches our regret lower bound.

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NeurIPS Conference 2025 Conference Paper

Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization

Shogo Iwazaki

This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret under a function drawn from a known Gaussian process (GP). Under a Mat\'ern kernel with some extent of smoothness, we show that the Gaussian process upper confidence bound (GP-UCB) algorithm achieves $\tilde{O}(\sqrt{T})$ cumulative regret with high probability. Furthermore, our analysis yields $O(\sqrt{T \ln^2 T})$ regret under a squared exponential kernel. These results fill the gap between the existing regret upper bound of GP-UCB and the current best upper bound provided by Scarlett [2018]. The key idea in our proof is to capture the concentration behavior of the input sequence realized by GP-UCB, enabling us to handle GP's information gain in a refined manner.

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NeurIPS Conference 2024 Conference Paper

No-Regret Bandit Exploration based on Soft Tree Ensemble Model

Shogo Iwazaki
Shinya Suzumura

We propose a novel stochastic bandit algorithm that employs reward estimates using a tree ensemble model. Specifically, our focus is on a soft tree model, a variant of the conventional decision tree that has undergone both practical and theoretical scrutiny in recent years. By deriving several non-trivial properties of soft trees, we extend the existing analytical techniques used for neural bandit algorithms to our soft tree-based algorithm. We demonstrate that our algorithm achieves a smaller cumulative regret compared to the existing ReLU-based neural bandit algorithms. We also show that this advantage comes with a trade-off: the hypothesis space of the soft tree ensemble model is more constrained than that of a ReLU-based neural network.

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NeurIPS Conference 2023 Conference Paper

Failure-Aware Gaussian Process Optimization with Regret Bounds

Shogo Iwazaki
Shion Takeno
Tomohiko Tanabe
Mitsuru Irie

Real-world optimization problems often require black-box optimization with observation failure, where we can obtain the objective function value if we succeed, otherwise, we can only obtain a fact of failure. Moreover, this failure region can be complex by several latent constraints, whose number is also unknown. For this problem, we propose a failure-aware Gaussian process upper confidence bound (F-GP-UCB), which only requires a mild assumption for the observation failure that an optimal solution lies on an interior of a feasible region. Furthermore, we show that the number of successful observations grows linearly, by which we provide the first regret upper bounds and the convergence of F-GP-UCB. We demonstrate the effectiveness of F-GP-UCB in several benchmark functions, including the simulation function motivated by material synthesis experiments.

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NeurIPS Conference 2022 Conference Paper

Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference

Vo Nguyen Le Duy
Shogo Iwazaki
Ichiro Takeuchi

Although a vast body of literature relates to image segmentation methods that use deep neural networks (DNNs), less attention has been paid to assessing the statistical reliability of segmentation results. In this study, we interpret the segmentation results as hypotheses driven by DNN (called DNN-driven hypotheses) and propose a method to quantify the reliability of these hypotheses within a statistical hypothesis testing framework. To this end, we introduce a conditional selective inference (SI) framework---a new statistical inference framework for data-driven hypotheses that has recently received considerable attention---to compute exact (non-asymptotic) valid p-values for the segmentation results. To use the conditional SI framework for DNN-based segmentation, we develop a new SI algorithm based on the homotopy method, which enables us to derive the exact (non-asymptotic) sampling distribution of DNN-driven hypothesis. We conduct several experiments to demonstrate the performance of the proposed method.

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ICML Conference 2021 Conference Paper

Active Learning for Distributionally Robust Level-Set Estimation

Yu Inatsu
Shogo Iwazaki
Ichiro Takeuchi

Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental} variables that have random variation following a certain distribution $P$. In such cases, an important task is to find the range of design variables $\bm x$ such that the function $f(\bm x, \bm w)$ has the desired properties by incorporating the random variation of the environmental variables $\bm w$. A natural measure of robustness is the probability that $f(\bm x, \bm w)$ exceeds a given threshold $h$, which is known as the \emph{probability threshold robustness} (PTR) measure in the literature on robust optimization. However, this robustness measure cannot be correctly evaluated when the distribution $P$ is unknown. In this study, we addressed this problem by considering the \textit{distributionally robust PTR} (DRPTR) measure, which considers the worst-case PTR within given candidate distributions. Specifically, we studied the problem of efficiently identifying a reliable set $H$, which is defined as a region in which the DRPTR measure exceeds a certain desired probability $\alpha$, which can be interpreted as a level set estimation (LSE) problem for DRPTR. We propose a theoretically grounded and computationally efficient active learning method for this problem. We show that the proposed method has theoretical guarantees on convergence and accuracy, and confirmed through numerical experiments that the proposed method outperforms existing methods.

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