arXiv subjects

Masahiro Nomura

Publications and source records attributed to Masahiro Nomura.

At least 37 records · Page 2Linked to original sources

arXiv2024

Phonon coherence and minimum thermal conductivity in disordered superlattice

Phonon coherence elucidates the propagation and interaction of phonon quantum states within superlattice, unveiling the wave-like nature and collective behaviors of phonons. Taking MoSe$_2$/WSe$_2$ lateral heterostructures as a model system, we demonstrate that the intricate interplay between wave-like and particle-like phonons, previously observed in perfect superlattice only, also occurs in disordered superlattice. By employing molecular dynamics simulation based on a highly accurate and efficient machine-learned potential constructed herein, we observe a non-monotonic dependence of the lattice thermal conductivity on the interface density in both perfect and disordered superlattice, with a global minimum occurring at relatively higher interface density for disordered superlattice. The counter-intuitive phonon coherence contribution can be characterized by the lagged self-similarity of the structural sequences in the disordered superlattice. Our findings extend the realm of coherent phonon transport from perfect superlattice to more general structures, which offers more flexibility in tuning thermal transport in superlattices.

cond-mat.mtrl-sci↗

arXiv2024

CMA-ES with Learning Rate Adaptation

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving continuous black-box optimization problems. A practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact on performance, especially for difficult tasks, such as solving multimodal or noisy problems. This study comprehensively explores the impact of learning rate on the CMA-ES performance and demonstrates the necessity of a small learning rate by considering ordinary differential equations. Thereafter, it discusses the setting of an ideal learning rate. Based on these discussions, we develop a novel learning rate adaptation mechanism for the CMA-ES that maintains a constant signal-to-noise ratio. Additionally, we investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate and with population size adaptation. The results show that the CMA-ES with the proposed learning rate adaptation works well for multimodal and/or noisy problems without extremely expensive learning rate tuning.

cs.NE↗

arXiv2024

CMA-ES for Discrete and Mixed-Variable Optimization on Sets of Points

Discrete and mixed-variable optimization problems have appeared in several real-world applications. Most of the research on mixed-variable optimization considers a mixture of integer and continuous variables, and several integer handlings have been developed to inherit the optimization performance of the continuous optimization methods to mixed-integer optimization. In some applications, acceptable solutions are given by selecting possible points in the disjoint subspaces. This paper focuses on the optimization on sets of points and proposes an optimization method by extending the covariance matrix adaptation evolution strategy (CMA-ES), termed the CMA-ES on sets of points (CMA-ES-SoP). The CMA-ES-SoP incorporates margin correction that maintains the generation probability of neighboring points to prevent premature convergence to a specific non-optimal point, which is an effective integer-handling technique for CMA-ES. In addition, because margin correction with a fixed margin value tends to increase the marginal probabilities for a portion of neighboring points more than necessary, the CMA-ES-SoP updates the target margin value adaptively to make the average of the marginal probabilities close to a predefined target probability. Numerical simulations demonstrated that the CMA-ES-SoP successfully optimized the optimization problems on sets of points, whereas the naive CMA-ES failed to optimize them due to premature convergence.

math.OC↗

arXiv2024

Effective Off-Policy Evaluation and Learning in Contextual Combinatorial Bandits

We explore off-policy evaluation and learning (OPE/L) in contextual combinatorial bandits (CCB), where a policy selects a subset in the action space. For example, it might choose a set of furniture pieces (a bed and a drawer) from available items (bed, drawer, chair, etc.) for interior design sales. This setting is widespread in fields such as recommender systems and healthcare, yet OPE/L of CCB remains unexplored in the relevant literature. Typical OPE/L methods such as regression and importance sampling can be applied to the CCB problem, however, they face significant challenges due to high bias or variance, exacerbated by the exponential growth in the number of available subsets. To address these challenges, we introduce a concept of factored action space, which allows us to decompose each subset into binary indicators. This formulation allows us to distinguish between the ''main effect'' derived from the main actions, and the ''residual effect'', originating from the supplemental actions, facilitating more effective OPE. Specifically, our estimator, called OPCB, leverages an importance sampling-based approach to unbiasedly estimate the main effect, while employing regression-based approach to deal with the residual effect with low variance. OPCB achieves substantial variance reduction compared to conventional importance sampling methods and bias reduction relative to regression methods under certain conditions, as illustrated in our theoretical analysis. Experiments demonstrate OPCB's superior performance over typical methods in both OPE and OPL.

stat.ML↗

arXiv2024

Natural Gradient Interpretation of Rank-One Update in CMA-ES

The covariance matrix adaptation evolution strategy (CMA-ES) is a stochastic search algorithm using a multivariate normal distribution for continuous black-box optimization. In addition to strong empirical results, part of the CMA-ES can be described by a stochastic natural gradient method and can be derived from information geometric optimization (IGO) framework. However, there are some components of the CMA-ES, such as the rank-one update, for which the theoretical understanding is limited. While the rank-one update makes the covariance matrix to increase the likelihood of generating a solution in the direction of the evolution path, this idea has been difficult to formulate and interpret as a natural gradient method unlike the rank-$μ$ update. In this work, we provide a new interpretation of the rank-one update in the CMA-ES from the perspective of the natural gradient with prior distribution. First, we propose maximum a posteriori IGO (MAP-IGO), which is the IGO framework extended to incorporate a prior distribution. Then, we derive the rank-one update from the MAP-IGO by setting the prior distribution based on the idea that the promising mean vector should exist in the direction of the evolution path. Moreover, the newly derived rank-one update is extensible, where an additional term appears in the update for the mean vector. We empirically investigate the properties of the additional term using various benchmark functions.

cs.NE↗

arXiv2024

Phonon dispersion of nanoscale honeycomb phononic crystal: gigahertz and terahertz spectroscopy comparison

Phonons-quantized vibrational modes in crystalline structures-govern phenomena ranging from thermal and mechanical transport to quantum mechanics. In recent years, a new class of artificial materials called phononic crystals has emerged, aiming to control phononic properties. These materials are created by introducing a superlattice structure on top of an already-existing atomic lattice. Typically, phononic crystals are described using a continuous model, in which effective elastic constants approximate potentials between atoms. This approximation, however, assumes the wavelengths of vibrations to be significantly greater than the interatomic distance. In this work, we experimentally investigate the behavior of a honeycomb silicon phononic crystal in the gigahertz range, where the continuum approximation holds, and in the terahertz range, where the phonon wavelengths are comparable to interatomic distances. Using Brillouin light scattering, we investigate the phonon dispersion of the phononic crystal in the gigahertz range, finding a close match with simulations based on the continuous model. Conversely, Raman spectroscopy reveals no difference between the phononic crystal, an unpatterned membrane, and a bulk silicon structure in the terahertz range, showing that the continuous model no longer holds at these higher frequencies.

cond-mat.mes-hall↗

arXiv2024

Piezoelectrically driven diamond phononic nanocavity by phonon-matching scheme for quantum applications

Efficiently exciting and controlling phonons in diamond nanoresonators represents a fundamental challenge for quantum applications. Here, we theoretically demonstrate the possibility to excite mechanical modes within a double-hybrid-cavity (DHC), formed by adjoining to a diamond cavity a second cavity, made of aluminum nitride. The latter is piezoelectric and serves as a microwave-to-phonon transducer, activating mechanical modes in the entire DHC. We show the process to match the cavities phononic properties, making them work coordinately in the DHC and obtaining a well confined mode. In the diamond part of the cavity, this mode replicates the fundamental mode of the individual diamond cavity, showing that the piezoelectric transducer doesn't alter the diamond individual fundamental mode. In the piezoelectric part, the strong confinement of stress and electric field results in a high piezoelectric coupling rate, demonstrating the effectiveness of a phononic cavity as a transducer. The study is contextualized in the framework of a quantum networking application, where the DHC serves as a spin qubit, exploiting the spin-mechanical coupling within diamond color centers.

cond-mat.mes-hall↗

arXiv2024

CMA-ES for Safe Optimization

In several real-world applications in medical and control engineering, there are unsafe solutions whose evaluations involve inherent risk. This optimization setting is known as safe optimization and formulated as a specialized type of constrained optimization problem with constraints for safety functions. Safe optimization requires performing efficient optimization without evaluating unsafe solutions. A few studies have proposed the optimization methods for safe optimization based on Bayesian optimization and the evolutionary algorithm. However, Bayesian optimization-based methods often struggle to achieve superior solutions, and the evolutionary algorithm-based method fails to effectively reduce unsafe evaluations. This study focuses on CMA-ES as an efficient evolutionary algorithm and proposes an optimization method termed safe CMA-ES. The safe CMA-ES is designed to achieve both safety and efficiency in safe optimization. The safe CMA-ES estimates the Lipschitz constants of safety functions transformed with the distribution parameters using the maximum norm of the gradient in Gaussian process regression. Subsequently, the safe CMA-ES projects the samples to the nearest point in the safe region constructed with the estimated Lipschitz constants. The numerical simulation using the benchmark functions shows that the safe CMA-ES successfully performs optimization, suppressing the unsafe evaluations, while the existing methods struggle to significantly reduce the unsafe evaluations.

cs.NE↗

arXiv2024

Hyperparameter Optimization Can Even be Harmful in Off-Policy Learning and How to Deal with It

There has been a growing interest in off-policy evaluation in the literature such as recommender systems and personalized medicine. We have so far seen significant progress in developing estimators aimed at accurately estimating the effectiveness of counterfactual policies based on biased logged data. However, there are many cases where those estimators are used not only to evaluate the value of decision making policies but also to search for the best hyperparameters from a large candidate space. This work explores the latter hyperparameter optimization (HPO) task for off-policy learning. We empirically show that naively applying an unbiased estimator of the generalization performance as a surrogate objective in HPO can cause an unexpected failure, merely pursuing hyperparameters whose generalization performance is greatly overestimated. We then propose simple and computationally efficient corrections to the typical HPO procedure to deal with the aforementioned issues simultaneously. Empirical investigations demonstrate the effectiveness of our proposed HPO algorithm in situations where the typical procedure fails severely.

cs.LG↗

arXiv2024

Off-Policy Evaluation of Slate Bandit Policies via Optimizing Abstraction

We study off-policy evaluation (OPE) in the problem of slate contextual bandits where a policy selects multi-dimensional actions known as slates. This problem is widespread in recommender systems, search engines, marketing, to medical applications, however, the typical Inverse Propensity Scoring (IPS) estimator suffers from substantial variance due to large action spaces, making effective OPE a significant challenge. The PseudoInverse (PI) estimator has been introduced to mitigate the variance issue by assuming linearity in the reward function, but this can result in significant bias as this assumption is hard-to-verify from observed data and is often substantially violated. To address the limitations of previous estimators, we develop a novel estimator for OPE of slate bandits, called Latent IPS (LIPS), which defines importance weights in a low-dimensional slate abstraction space where we optimize slate abstractions to minimize the bias and variance of LIPS in a data-driven way. By doing so, LIPS can substantially reduce the variance of IPS without imposing restrictive assumptions on the reward function structure like linearity. Through empirical evaluation, we demonstrate that LIPS substantially outperforms existing estimators, particularly in scenarios with non-linear rewards and large slate spaces.

stat.ML↗

arXiv2024

Marginal Probability-Based Integer Handling for CMA-ES Tackling Single-and Multi-Objective Mixed-Integer Black-Box Optimization

This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing integer handling for the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple integer handling for the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method. Furthermore, in order to demonstrate the generality of the idea of the proposed method, in addition to the single-objective optimization case, we incorporate it into multi-objective CMA-ES and verify its performance on bi-objective mixed-integer benchmark problems.

cs.NE↗

arXiv2023

Diamond optomechanical cavity with a color center for microwave-to-optical quantum interfaces

Quantum transduction between microwave and optical photons plays a key role in quantum communication among remote qubits. Although the quantum transduction schemes generating communication photons have been successfully demonstrated by using optomechanical interfaces, the low conversion efficiency remains an obstacle to the implementation of a quantum network consisting of multiple qubits. Here, we present an efficient quantum transduction scheme using a one-dimensional diamond optomechanical crystal cavity tuned at a color-center emission without optomechanical coupling. The optomechanical crystal cavity incorporates a thin aluminum nitride (AlN) pad piezoelectric coupler near the concentrator cavity region, while retaining ultrasmall mechanical and optical mode volumes of about 1.5 \times 10^{-4} and ~0.2(λ/n)^3, respectively. The energy level of a coherent color-center electron is manipulated by a strong mechanical-mode-color-center electron-coupling rate up to 16.4MHz. In our system, we theoretically predict that the population-conversion efficiency from a single microwave photon into an optical photon can reach 15% combined with current technologies. The coherent conversion efficiency is over 10% with a reasonably pure decay time of T^2_{*} > 10 ns. Our results imply that an atomic color center strongly coupled to the optomechanical crystal cavity will offer a highly efficient quantum transduction platform.

quant-ph↗

arXiv2023

CMA-ES with Learning Rate Adaptation: Can CMA-ES with Default Population Size Solve Multimodal and Noisy Problems?

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving black-box continuous optimization problems. One practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact, especially for difficult tasks such as solving multimodal or noisy problems. In this study, we investigate whether the CMA-ES with default population size can solve multimodal and noisy problems. To perform this investigation, we develop a novel learning rate adaptation mechanism for the CMA-ES, such that the learning rate is adapted so as to maintain a constant signal-to-noise ratio. We investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate. The results demonstrate that, when the proposed learning rate adaptation is used, the CMA-ES with default population size works well on multimodal and/or noisy problems, without the need for extremely expensive learning rate tuning.

cs.NE↗

arXiv2023

Planar-type silicon thermoelectric generator with phononic nanostructures for 100 μW energy harvesting

Energy harvesting is essential for the internet-of-things networks where a tremendous number of sensors require power. Thermoelectric generators (TEGs), especially those based on silicon (Si), are a promising source of clean and sustainable energy for these sensors. However, the reported performance of planar-type Si TEGs never exceeded power factors of 0.1 $μ Wcm^{-2} K^{-2}$ due to the poor thermoelectric performance of Si and the suboptimal design of the devices. Here, we report a planar-type Si TEG with a power factor of 1.3 $μ Wcm^{-2} K^{-2}$ around room temperature. The increase in thermoelectric performance of Si by nanostructuring based on the phonon-glass electron-crystal concept and optimized three-dimensional heat-guiding structures resulted in a significant power factor. In-field testing demonstrated that our Si TEG functions as a 100-$μW$-class harvester. This result is an essential step toward energy harvesting with a low-environmental load and cost-effective material with high throughput, a necessary condition for energy-autonomous sensor nodes for the trillion sensors universe.

physics.app-ph↗

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.

cs.LG↗

arXiv2023

(1+1)-CMA-ES with Margin for Discrete and Mixed-Integer Problems

The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient continuous black-box optimization method. The CMA-ES possesses many attractive features, including invariance properties and a well-tuned default hyperparameter setting. Moreover, several components to specialize the CMA-ES have been proposed, such as noise handling and constraint handling. To utilize these advantages in mixed-integer optimization problems, the CMA-ES with margin has been proposed. The CMA-ES with margin prevents the premature convergence of discrete variables by the margin correction, in which the distribution parameters are modified to leave the generation probability for changing the discrete variable. The margin correction has been applied to ($μ/μ_\mathrm{w}$,$λ$)-CMA-ES, while this paper introduces the margin correction into (1+1)-CMA-ES, an elitist version of CMA-ES. The (1+1)-CMA-ES is often advantageous for unimodal functions and can be computationally less expensive. To tackle the performance deterioration on mixed-integer optimization, we use the discretized elitist solution as the mean of the sampling distribution and modify the margin correction not to move the elitist solution. The numerical simulation using benchmark functions on mixed-integer, integer, and binary domains shows that (1+1)-CMA-ES with margin outperforms the CMA-ES with margin and is better than or comparable with several specialized methods to a particular search domain.

cs.NE↗

arXiv2023

Magic angle in thermal conductivity of twisted bilayer graphene

We report a local minimum in thermal conductivity in twisted bilayer graphene (TBG) at the angle of 1.08$^\circ$, which corresponds to the 'magic angle' in the transition of several other reported properties. Within the supercell of a moiré lattice, different stacking modes generate phonon scattering sites which reduce the thermal conductivity of TBG. The thermal magic angle arises from the competition between the delocalization of atomic vibrational amplitudes and stresses on one hand, and the increased AA stacking density on the other hand. The former effect weakens the scattering strength of a single scatterer while the latter one increases the density of scatterers. The combination of these two effects eventually leads to the apparition of the highlighted irregularity in heat conduction. The manifestation of a magic angle, disclosing new thermal mechanisms at nanoscale, further uncovers the unique physics of two-dimensional materials.

cond-mat.mes-hall↗

arXiv2023

CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization

This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing modification to the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple modification of the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method.

cs.NE↗