arXiv subjects

Shion Takeno

Publications and source records attributed to Shion Takeno.

At least 19 recordsLinked to original sources

arXiv2026

Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization

This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization. The known regret upper bounds for the widely used GP batched upper confidence bound and GP batched Thompson sampling (GP-BTS) suffer from a multiplicative factor with respect to the batch size $Q$. To avoid this degradation, existing analyses require a polynomial number of uncertainty sampling (US) for $Q$ at the beginning of optimization. However, this initial US phase is often ineffective in practice. This paper shows that the regret upper bound without the multiplicative factor on $Q$ can be achieved without the initial US phase, using GP-BTS as an example. Furthermore, we show much better regret upper bounds in the noiseless setting than in the noisy setting, as in the sequential GP bandit setting.

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arXiv2026

Millimeter-wave adaptive optics: Demonstrating closed-loop correction for lowest Zernike modes

We report on a five-element prototype wavefront sensor for millimeter-wave adaptive optics (MAO), enabling closed-loop correction of tip-tilt and defocus via secondary mirror (M2) displacement. MAO is essential for large ground-based millimeter/submillimeter telescopes to maintain surface accuracy under wind and thermal distortions. Our sensor, based on radio interferometry, measures excess path lengths from the primary mirror to a focal-plane receiver. A previous two-element prototype achieved < 10 um accuracy at the Nobeyama 45 m telescope. The new five-element system, operating at 20 GHz, was installed on the same telescope. A ``Moon-edge'' experiment confirmed detection of wavefront gradients through strong correlation with continuum flux. Implementing a PI controller closed the sensor-M2 loop, stably suppressing the lowest Zernike modes. This approach establishes a foundation for metrology in future large-aperture submillimeter facilities such as AtLAST/LST.

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arXiv2026

Anti-windup PI controller for millimeter-wave adaptive optics: a Nobeyama 45 m radio telescope simulation

This work addresses the control problem for Millimeter-wave Adaptive Optics (MAO), which we define as compensating for the distance variation between the primary reflector (M1) and the receiver. We utilize a measurement system developed by Tamura et al. to track these variations. The challenge is formalized as an asymptotic constant disturbance suppression problem. We demonstrate that an anti-windup proportional-integral (AWPI) controller effectively solves this problem while respecting the physical movement constraints of the optical driving system. Simulation results, based on the Nobeyama 45-m Telescope with a two-axis translating sub-reflector (M2), validate the performance of the proposed AWPI approach.

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arXiv2026

Randomized Kriging Believer for Parallel Bayesian Optimization with Regret Bounds

We consider the optimization problem of an expensive-to-evaluate black-box function, in which we can obtain noisy function values in parallel. For this problem, parallel Bayesian optimization (PBO) is a promising approach, which aims to optimize with fewer function evaluations by selecting a diverse input set for parallel evaluation. However, existing PBO methods suffer from poor practical performance or lack theoretical guarantees. In this study, we propose a PBO method, called randomized kriging believer (KB), based on a well-known KB heuristic and inheriting the advantages of the original KB: low computational complexity, a simple implementation, versatility across various BO methods, and applicability to asynchronous parallelization. Furthermore, we show that our randomized KB achieves Bayesian expected regret guarantees. We demonstrate the effectiveness of the proposed method through experiments, including those on real-data emulators.

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arXiv2026

On Regret Bounds of Thompson Sampling for Bayesian Optimization

We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compared with the GP upper confidence bound (GP-UCB) with established high-probability and expected regret bounds, most analyses of GP-TS have been limited to expected regret. Moreover, whether the recent analyses of GP-UCB for the lenient regret and the improved cumulative regret upper bound can be applied to GP-TS remains unclear. To fill these gaps, this paper shows several regret bounds: (i) a regret lower bound for GP-TS, which implies that GP-TS suffers from a polynomial dependence on $1/δ$ with probability $δ$, (ii) an upper bound of the second moment of cumulative regret, which directly suggests an improved regret upper bound on $δ$, (iii) expected lenient regret upper bounds, and (iv) an improved cumulative regret upper bound on the time horizon $T$. Along the way, we provide several useful lemmas, including a relaxation of the necessary condition from recent analysis to obtain improved regret upper bounds on $T$.

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arXiv2026

Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee

This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments.

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arXiv2026

Safe Distributionally Robust Feature Selection under Covariate Shift

In practical machine learning, the environments encountered during the model development and deployment phases often differ, especially when a model is used by many users in diverse settings. Learning models that maintain reliable performance across plausible deployment environments is known as distributionally robust (DR) learning. In this work, we study the problem of distributionally robust feature selection (DRFS), with a particular focus on sparse sensing applications motivated by industrial needs. In practical multi-sensor systems, a shared subset of sensors is typically selected prior to deployment based on performance evaluations using many available sensors. At deployment, individual users may further adapt or fine-tune models to their specific environments. When deployment environments differ from those anticipated during development, this strategy can result in systems lacking sensors required for optimal performance. To address this issue, we propose safe-DRFS, a novel approach that extends safe screening from conventional sparse modeling settings to a DR setting under covariate shift. Our method identifies a feature subset that encompasses all subsets that may become optimal across a specified range of input distribution shifts, with finite-sample theoretical guarantees of no false feature elimination.

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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

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

Distributionally Robust Active Learning for Gaussian Process Regression

Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with fewer data labels, is an important problem. However, existing AL methods do not theoretically guarantee prediction accuracy for target distribution. Furthermore, as discussed in the distributionally robust learning literature, specifying the target distribution is often difficult. Thus, this paper proposes two AL methods that effectively reduce the worst-case expected error for GPR, which is the worst-case expectation in target distribution candidates. We show an upper bound of the worst-case expected squared error, which suggests that the error will be arbitrarily small by a finite number of data labels under mild conditions. Finally, we demonstrate the effectiveness of the proposed methods through synthetic and real-world datasets.

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arXiv2025

Dose-finding design based on level set estimation in phase I cancer clinical trials

The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded as a level set estimation (LSE) problem whose objective is to determine the regions where an unknown function value is above or below a given threshold. Then, we propose a novel dose-finding design in the framework of LSE. The proposed design determines the next dose on the basis of an acquisition function incorporating uncertainty in the posterior distribution of the dose-toxicity curve as well as overdose control. Simulation experiments show that the proposed LSE design achieves a higher accuracy in estimating the MTD and involves a lower risk of overdosing allocation compared to existing designs, thereby indicating that it provides an effective methodology for phase I cancer clinical trial design.

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arXiv2025

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

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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arXiv2024

Active Learning for Level Set Estimation Using Randomized Straddle Algorithms

Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and black-box, the \textit{straddle} algorithm, which is a representative heuristic for LSE based on Gaussian process models, and its extensions having theoretical guarantees have been developed. However, many of existing methods include a confidence parameter $β^{1/2}_t$ that must be specified by the user, and methods that choose $β^{1/2}_t$ heuristically do not provide theoretical guarantees. In contrast, theoretically guaranteed values of $β^{1/2}_t$ need to be increased depending on the number of iterations and candidate points, and are conservative and not good for practical performance. In this study, we propose a novel method, the \textit{randomized straddle} algorithm, in which $β_t$ in the straddle algorithm is replaced by a random sample from the chi-squared distribution with two degrees of freedom. The confidence parameter in the proposed method has the advantages of not needing adjustment, not depending on the number of iterations and candidate points, and not being conservative. Furthermore, we show that the proposed method has theoretical guarantees that depend on the sample complexity and the number of iterations. Finally, we confirm the usefulness of the proposed method through numerical experiments using synthetic and real data.

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arXiv2024

Distributionally Robust Safe Sample Elimination under Covariate Shift

We consider a machine learning setup where one training dataset is used to train multiple models across slightly different data distributions. This occurs when customized models are needed for various deployment environments. To reduce storage and training costs, we propose the DRSSS method, which combines distributionally robust (DR) optimization and safe sample screening (SSS). The key benefit of this method is that models trained on the reduced dataset will perform the same as those trained on the full dataset for all possible different environments. In this paper, we focus on covariate shift as a type of data distribution change and demonstrate the effectiveness of our method through experiments.

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arXiv2024

Near-Optimal Algorithm for Non-Stationary Kernelized Bandits

This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Matérn kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost. Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.

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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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arXiv2023

Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty

In this study, we propose a novel multi-objective Bayesian optimization (MOBO) method to efficiently identify the Pareto front (PF) defined by risk measures for black-box functions under the presence of input uncertainty (IU). Existing BO methods for Pareto optimization in the presence of IU are risk-specific or without theoretical guarantees, whereas our proposed method addresses general risk measures and has theoretical guarantees. The basic idea of the proposed method is to assume a Gaussian process (GP) model for the black-box function and to construct high-probability bounding boxes for the risk measures using the GP model. Furthermore, in order to reduce the uncertainty of non-dominated bounding boxes, we propose a method of selecting the next evaluation point using a maximin distance defined by the maximum value of a quasi distance based on bounding boxes. As theoretical analysis, we prove that the algorithm can return an arbitrary-accurate solution in a finite number of iterations with high probability, for various risk measures such as Bayes risk, worst-case risk, and value-at-risk. We also give a theoretical analysis that takes into account approximation errors because there exist non-negligible approximation errors (e.g., finite approximation of PFs and sampling-based approximation of bounding boxes) in practice. We confirm that the proposed method outperforms compared with existing methods not only in the setting with IU but also in the setting of ordinary MOBO through numerical experiments.

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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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