PID controllers are widely used in control systems because of their simplicity and effectiveness. Although advanced optimization techniques such as Bayesian Optimization and Differential Evolution have been applied to address the challenges of automatic tuning of PID controllers, the influence of initial system states on convergence and the balance between exploration and exploitation remains underexplored. Moreover, experimenting the influence directly on real cyber-physical systems such as mobile robots is crucial for deriving realistic insights. In the present paper, a novel framework is introduced to evaluate the impact of systematically varying these factors on the PID auto-tuning processes that utilize Bayesian Optimization and Differential Evolution. Testing was conducted on two distinct PID-controlled robotic platforms, an omnidirectional robot and a differential drive mobile robot, to assess the effects on convergence rate, settling time, rise time, and overshoot percentage. As a result, the experimental outcomes yield evidence on the effects of the systematic variations, thereby providing an empirical basis for future research studies in the field.
X-ray absorption near edge structure (XANES) spectroscopy is a powerful technique for characterizing the chemical state and symmetry of individual elements within materials, but requires collecting data at many energy points which can be time-consuming. While adaptive sampling methods exist for efficiently collecting spectroscopic data, they often lack domain-specific knowledge about XANES spectra structure. Here we demonstrate a knowledge-injected Bayesian optimization approach for adaptive XANES data collection that incorporates understanding of spectral features like absorption edges and pre-edge peaks. We show this method accurately reconstructs the absorption edge of XANES spectra using only 15-20% of the measurement points typically needed for conventional sampling, while maintaining the ability to determine the x-ray energy of the sharp peak after absorption edge with errors less than 0.03 eV, the absorption edge with errors less than 0.1 eV; and overall root-mean-square errors less than 0.005 compared to compared to traditionally sampled spectra. Our experiments on battery materials and catalysts demonstrate the method's effectiveness for both static and dynamic XANES measurements, improving data collection efficiency and enabling better time resolution for tracking chemical changes. This approach advances the degree of automation in XANES experiments reducing the common errors of under- or over-sampling points in near the absorption edge and enabling dynamic experiments that require high temporal resolution or limited measurement time.
Bayesian Optimization (BO) has been recognized for its effectiveness in optimizing expensive and complex objective functions. Recent advancements in Latent Bayesian Optimization (LBO) have shown promise by integrating generative models such as variational autoencoders (VAEs) to manage the complexity of high-dimensional and structured data spaces. However, existing LBO approaches often suffer from the value discrepancy problem, which arises from the reconstruction gap between input and latent spaces. This value discrepancy problem propagates errors throughout the optimization process, leading to suboptimal outcomes. To address this issue, we propose a Normalizing Flow-based Bayesian Optimization (NF-BO), which utilizes normalizing flow as a generative model to establish one-to-one encoding function from the input space to the latent space, along with its left-inverse decoding function, eliminating the reconstruction gap. Specifically, we introduce SeqFlow, an autoregressive normalizing flow for sequence data. In addition, we develop a new candidate sampling strategy that dynamically adjusts the exploration probability for each token based on its importance. Through extensive experiments, our NF-BO method demonstrates superior performance in molecule generation tasks, significantly outperforming both traditional and recent LBO approaches.
Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the exploration-exploitation process toward finding global optimum. While Gaussian processes (GPs) are commonly employed as surrogates of the unknown objective function, recent studies have highlighted the potential of Bayesian neural networks (BNNs) as scalable and flexible alternatives. Moreover, incorporating gradient observations into GPs, when available, has been shown to improve BO performance. However, the use of gradients within BNN surrogates remains unexplored. By leveraging automatic differentiation, gradient information can be seamlessly integrated into BNN training, resulting in more informative surrogates for BO. We propose a gradient-informed loss function for BNN training, effectively augmenting function observations with local gradient information. The effectiveness of this approach is demonstrated on well-known benchmarks in terms of improved BNN predictions and faster BO convergence as the number of decision variables increases.
Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high number of data points required to fit the model, this limitation can be addressed if the problem satisfies simplifying assumptions. Axis-aligned subspace approaches, where few dimensions have a significant impact on the objective, motivated several algorithms for high-dimensional BO . However, the validity of this assumption is rarely verified, and the assumption is rarely exploited to its full extent. We propose a group testing ( GT) approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective, then terminates once active dimensions are identified. To that end, we extend the well-established GT theory to functions over continuous domains. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By leveraging the axis-aligned subspace assumption, GTBO outperforms state-of-the-art methods on benchmarks satisfying the assumption of axis-aligned subspaces, while offering improved interpretability.
Existing portfolio management approaches are often black-box models due to safety and commercial issues in the industry. However, their performance can vary considerably whenever market conditions or internal trading strategies change. Furthermore, evaluating these non-transparent systems is expensive, where certain budgets limit observations of the systems. Therefore, optimizing performance while controlling the potential risk of these financial systems has become a critical challenge. This work presents a novel Bayesian optimization framework to optimize black-box portfolio management models under limited observations. In conventional Bayesian optimization settings, the objective function is to maximize the expectation of performance metrics. However, simply maximizing performance expectations leads to erratic optimization trajectories, which exacerbate risk accumulation in portfolio management. Meanwhile, this can lead to misalignment between the target distribution and the actual distribution of the black-box model. To mitigate this problem, we propose an adaptive weight Lagrangian estimator considering dual objective, which incorporates maximizing model performance and minimizing variance of model observations. Extensive experiments demonstrate the superiority of our approach over five backtest settings with three black-box stock portfolio management models. Ablation studies further verify the effectiveness of the proposed estimator.
Bayesian optimization (BO) is a widely used algorithm for solving expensive black-box optimization problems. However, its performance decreases significantly on high-dimensional problems due to the inherent high-dimensionality of the acquisition function. In the proposed algorithm, we adaptively dropout the variables of the acquisition function along the iterations. By gradually reducing the dimension of the acquisition function, the proposed approach has less and less difficulty to optimize the acquisition function. Numerical experiments demonstrate that AdaDropout effectively tackle high-dimensional challenges and improve solution quality where standard Bayesian optimization methods often struggle. Moreover, it achieves superior results when compared with state-of-the-art high-dimensional Bayesian optimization approaches. This work provides a simple yet efficient solution for high-dimensional expensive optimization.
Temporal Point Processes (TPPs) are widely used for modeling event sequences in various medical domains, such as disease onset prediction, progression analysis, and clinical decision support. Although TPPs effectively capture temporal dynamics, their lack of interpretability remains a critical challenge. Recent advancements have introduced interpretable TPPs. However, these methods fail to incorporate numerical features, thereby limiting their ability to generate precise predictions. To address this issue, we propose Hybrid-Rule Temporal Point Processes (HRTPP), a novel framework that integrates temporal logic rules with numerical features, improving both interpretability and predictive accuracy in event modeling. HRTPP comprises three key components: basic intensity for intrinsic event likelihood, rule-based intensity for structured temporal dependencies, and numerical feature intensity for dynamic probability modulation. To effectively discover valid rules, we introduce a two-phase rule mining strategy with Bayesian optimization. To evaluate our method, we establish a multi-criteria assessment framework, incorporating rule validity, model fitting, and temporal predictive accuracy. Experimental results on real-world medical datasets demonstrate that HRTPP outperforms state-of-the-art interpretable TPPs in terms of predictive performance and clinical interpretability. In case studies, the rules extracted by HRTPP explain the disease progression, offering valuable contributions to medical diagnosis.
Motivated by the growing need for black-box optimization and data privacy, we introduce a collaborative Bayesian optimization (BO) framework that addresses both of these challenges. In this framework agents work collaboratively to optimize a function they only have oracle access to. In order to mitigate against communication and privacy constraints, agents are not allowed to share their data but can share their Gaussian process (GP) surrogate models. To enable collaboration under these constraints, we construct a central model to approximate the objective function by leveraging the concept of Wasserstein barycenters of GPs. This central model integrates the shared models without accessing the underlying data. A key aspect of our approach is a collaborative acquisition function that balances exploration and exploitation, allowing for the optimization of decision variables collaboratively in each iteration. We prove that our proposed algorithm is asymptotically consistent and that its implementation via Monte Carlo methods is numerically accurate. Through numerical experiments, we demonstrate that our approach outperforms other baseline collaborative frameworks and is competitive with centralized approaches that do not consider data privacy.
This work aims at developing new methodologies to optimize computational costly complex systems (e.g., aeronautical engineering systems). The proposed surrogate-based method (often called Bayesian optimization) uses adaptive sampling to promote a trade-off between exploration and exploitation. Our in-house implementation, called SEGOMOE, handles a high number of design variables (continuous, discrete or categorical) and nonlinearities by combining mixtures of experts for the objective and/or the constraints. Additionally, the method handles multi-objective optimization settings, as it allows the construction of accurate Pareto fronts with a minimal number of function evaluations. Different infill criteria have been implemented to handle multiple objectives with or without constraints. The effectiveness of the proposed method was tested on practical aeronautical applications within the context of the European Project AGILE 4.0 and demonstrated favorable results. A first example concerns a retrofitting problem where a comparison between two optimizers have been made. A second example introduces hierarchical variables to deal with architecture system in order to design an aircraft family. The third example increases drastically the number of categorical variables as it combines aircraft design, supply chain and manufacturing process. In this article, we show, on three different realistic problems, various aspects of our optimization codes thanks to the diversity of the treated aircraft problems.
Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling methods and loss function weights for different PDEs, which reduces the efficiency of the solvers. In this paper, we pro- pose a general multi-stage framework, i.e. BO-SA-PINNs to alleviate this issue. In the first stage, Bayesian optimization (BO) is used to select hyperparameters for the training process, and based on the results of the pre-training, the network architecture, learning rate, sampling points distribution and loss function weights suitable for the PDEs are automatically determined. The proposed hyperparameters search space based on experimental results can enhance the efficiency of BO in identifying optimal hyperparameters. After selecting the appropriate hyperparameters, we incorporate a global self-adaptive (SA) mechanism the second stage. Using the pre-trained model and loss information in the second-stage training, the exponential moving average (EMA) method is employed to optimize the loss function weights, and residual-based adaptive refinement with distribution (RAR-D) is used to optimize the sampling points distribution. In the third stage, L-BFGS is used for stable training. In addition, we introduce a new activation function that enables BO-SA-PINNs to achieve higher accuracy. In numerical experiments, we conduct comparative and ablation experiments to verify the performance of the model on Helmholtz, Maxwell, Burgers and high-dimensional Poisson equations. The comparative experiment results show that our model can achieve higher accuracy and fewer iterations in test cases, and the ablation experiments demonstrate the positive impact of every improvement.
Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.
Bayesian optimization is an advanced tool to perform ecient global optimization It consists on enriching iteratively surrogate Kriging models of the objective and the constraints both supposed to be computationally expensive of the targeted optimization problem Nowadays efficient extensions of Bayesian optimization to solve expensive multiobjective problems are of high interest The proposed method in this paper extends the super efficient global optimization with mixture of experts SEGOMOE to solve constrained multiobjective problems To cope with the illposedness of the multiobjective inll criteria different enrichment procedures using regularization techniques are proposed The merit of the proposed approaches are shown on known multiobjective benchmark problems with and without constraints The proposed methods are then used to solve a biobjective application related to conceptual aircraft design with ve unknown design variables and three nonlinear inequality constraints The preliminary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.
The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and evaluations might fail. The former challenge is addressed by Surrogate-Based Optimization (SBO) algorithms, in particular Bayesian Optimization (BO) using Gaussian Process (GP) models. An overview is provided of how BO can deal with challenges specific to architecture optimization, such as design variable hierarchy and multiple objectives: specific measures include ensemble infills and a hierarchical sampling algorithm. Evaluations might fail due to non-convergence of underlying solvers or infeasible geometry in certain areas of the design space. Such failed evaluations, also known as hidden constraints, pose a particular challenge to SBO/BO, as the surrogate model cannot be trained on empty results. This work investigates various strategies for satisfying hidden constraints in BO algorithms. Three high-level strategies are identified: rejection of failed points from the training set, replacing failed points based on viable (non-failed) points, and predicting the failure region. Through investigations on a set of test problems including a jet engine architecture optimization problem, it is shown that best performance is achieved with a mixed-discrete GP to predict the Probability of Viability (PoV), and by ensuring selected infill points satisfy some minimum PoV threshold. This strategy is demonstrated by solving a jet engine architecture problem that features at 50% failure rate and could not previously be solved by a BO algorithm. The developed BO algorithm and used test problems are available in the open-source Python library SBArchOpt.
Tradable credit schemes (TCS) are an increasingly studied alternative to congestion pricing, given their revenue neutrality and ability to address issues of equity through the initial credit allocation. Modeling TCS to aid future design and implementation is associated with challenges involving user and market behaviors, demand-supply dynamics, and control mechanisms. In this paper, we focus on the latter and address the day-to-day dynamic tolling problem under TCS, which is formulated as a discrete-time Markov Decision Process and solved using reinforcement learning (RL) algorithms. Our results indicate that RL algorithms achieve travel times and social welfare comparable to the Bayesian optimization benchmark, with generalization across varying capacities and demand levels. We further assess the robustness of RL under different hyperparameters and apply regularization techniques to mitigate action oscillation, which generates practical tolling strategies that are transferable under day-to-day demand and supply variability. Finally, we discuss potential challenges such as scaling to large networks, and show how transfer learning can be leveraged to improve computational efficiency and facilitate the practical deployment of RL-based TCS solutions.
This study focuses on mixed-variable black-box optimization (MV-BBO), addressing continuous, integer, and categorical variables. Many real-world MV-BBO problems involve dependencies among these different types of variables, requiring efficient methods to optimize them simultaneously. Recently, stochastic optimization methods leveraging the mechanism of the covariance matrix adaptation evolution strategy have shown promising results in mixed-integer or mixed-category optimization. However, such methods cannot handle the three types of variables simultaneously. In this study, we propose CatCMA with Margin (CatCMAwM), a stochastic optimization method for MV-BBO that jointly optimizes continuous, integer, and categorical variables. CatCMAwM is developed by incorporating a novel integer handling into CatCMA, a mixed-category black-box optimization method employing a joint distribution of multivariate Gaussian and categorical distributions. The proposed integer handling is carefully designed by reviewing existing integer handlings and following the design principles of CatCMA. Even when applied to mixed-integer problems, it stabilizes the marginal probability and improves the convergence performance of continuous variables. Numerical experiments show that CatCMAwM effectively handles the three types of variables, outperforming state-of-the-art Bayesian optimization methods and baselines that simply incorporate existing integer handlings into CatCMA.
Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity in computing the Gaussian process (GP) surrogate model. In large-budget scenarios, directly employing the standard GP model faces significant challenges in computational time and resource requirements. In this paper, we propose a novel approach, gradient-based sample selection Bayesian Optimization (GSSBO), to enhance the computational efficiency of BO. The GP model is constructed on a selected set of samples instead of the whole dataset. These samples are selected by leveraging gradient information to maintain diversity and representation. We provide a theoretical analysis of the gradient-based sample selection strategy and obtain explicit sublinear regret bounds for our proposed framework. Extensive experiments on synthetic and real-world tasks demonstrate that our approach significantly reduces the computational cost of GP fitting in BO while maintaining optimization performance comparable to baseline methods.
Large Language Models (LLMs) can encode complex relationships in their latent spaces, yet harnessing them for optimization under uncertainty remains challenging. We address this gap with a novel architecture that reframes LLM finetuning as Gaussian process (GP) marginal likelihood optimization via deep kernel methods. We introduce LLM-based deep kernels, jointly optimized with GPs to preserve the benefits of both - LLMs to provide a rich and flexible input space for Bayesian optimization and - GPs to model this space with predictive uncertainty for more efficient sampling. Applied to Buchwald-Hartwig reaction optimization, our method nearly doubles the discovery rate of high-performing reactions compared to static LLM embeddings (from 24% to 43% coverage of the top 5% reactions in just 50 optimization iterations). We also observe a 14% improvement over domain-specific representations without requiring specialized features. Extensive empirical evaluation across 19 benchmarks - ranging from general chemistry to reaction and molecular property optimization - demonstrates our method's robustness, generality, and consistent improvements across: (1) tasks, (2) LLM architectures (encoder, decoder, encoder-decoder), (3) pretraining domains (chemistry-related or general-purpose) and (4) hyperparameter settings (tuned once on a single dataset). Finally, we explain these improvements: joint LLM-GP optimization through marginal likelihood implicitly performs contrastive learning, aligning representations to produce (1) better-structured embedding spaces, (2) improved uncertainty calibration, and (3) more efficient sampling - without requiring any external loss. This work provides both practical advances in sample-efficient optimization and insights into what makes effective Bayesian optimization.
Solving black-box optimization problems with Ising machines is increasingly common in materials science. However, their application to crystal structure prediction (CSP) is still ineffective due to symmetry agnostic encoding of atomic coordinates. We introduce CRYSIM, an algorithm that encodes the space group, the Wyckoff positions combination, and coordinates of independent atomic sites as separate variables. This encoding reduces the search space substantially by exploiting the symmetry in space groups. When CRYSIM is interfaced to Fixstars Amplify, a GPU-based Ising machine, its prediction performance was competitive with CALYPSO and Bayesian optimization for crystals containing more than 150 atoms in a unit cell. Although it is not realistic to interface CRYSIM to current small-scale quantum devices, it has the potential to become the standard CSP algorithm in the coming quantum age.
Automated experimentation has the potential to revolutionize scientific discovery, but its effectiveness depends on well-defined optimization targets, which are often uncertain or probabilistic in real-world settings. In this work, we demonstrate the application of Multi-Objective Bayesian Optimization (MOBO) to balance multiple, competing rewards in autonomous experimentation. Using scanning probe microscopy (SPM) imaging, one of the most widely used and foundational SPM modes, we show that MOBO can optimize imaging parameters to enhance measurement quality, reproducibility, and efficiency. A key advantage of this approach is the ability to compute and analyze the Pareto front, which not only guides optimization but also provides physical insights into the trade-offs between different objectives. Additionally, MOBO offers a natural framework for human-in-the-loop decision-making, enabling researchers to fine-tune experimental trade-offs based on domain expertise. By standardizing high-quality, reproducible measurements and integrating human input into AI-driven optimization, this work highlights MOBO as a powerful tool for advancing autonomous scientific discovery.