Bayesian Optimization (BO) machine learning method is increasingly used to guide experimental optimization tasks in materials science. To emulate the large number of input variables and noise-containing results in experimental materials research, we perform batch BO simulation of six design variables with a range of noise levels. Two test cases relevant for materials science problems are examined: a needle-in-a-haystack case (Ackley function) that may be encountered in, e.g., molecule optimizations, and a smooth landscape with a local optimum in addition to the global optimum (Hartmann function) that may be encountered in, e.g., material composition optimization. We show learning curves, performance metrics, and visualization to effectively track the optimization progression and evaluate how the optimization outcomes are affected by noise, batch-picking method, choice of acquisition function, and exploration hyperparameter values. We find that the effects of noise depend on the problem landscape: noise degrades the optimization results of a needle-in-a-haystack search (Ackley) dramatically more. However, with increasing noise, we observe an increasing probability of landing on the local optimum in Hartmann. Therefore, prior knowledge of the problem domain structure and noise level is essential when designing BO for materials research experiments. Synthetic data studies -- with known ground truth and controlled noise levels -- enable us to isolate and evaluate the impact of different batch BO components, {\it e.g.}, acquisition policy, objective metrics, and hyperparameter values, before transitioning to the inherent uncertainties of real experimental systems. The results and methodology of this study will facilitate a greater utilization of BO in guiding experimental materials research, specifically in settings with a large number of design variables to optimize.
Discovering novel materials with desired properties is essential for driving innovation. Industry 4.0 and smart manufacturing have promised transformative advances in this area through real-time data integration and automated production planning and control. However, the reliance on automation alone has often fallen short, lacking the flexibility needed for complex processes. To fully unlock the potential of smart manufacturing, we must evolve from automation to autonomous systems that go beyond rigid programming and can dynamically optimize the search for solutions. Current discovery approaches are often slow, requiring numerous trials to find optimal combinations, and costly, particularly when optimizing multiple properties simultaneously. This paper proposes a Bayesian multi-objective sequential decision-making (BMSDM) framework that can intelligently select experiments as manufacturing progresses, guiding us toward the discovery of optimal design faster and more efficiently. The framework leverages sequential learning through Bayesian Optimization, which iteratively refines a statistical model representing the underlying manufacturing process. This statistical model acts as a surrogate, allowing for efficient exploration and optimization without requiring numerous real-world experiments. This approach can significantly reduce the time and cost of data collection required by traditional experimental designs. The proposed framework is compared with traditional DoE methods and two other multi-objective optimization methods. Using a manufacturing dataset, we evaluate and compare the performance of these approaches across five evaluation metrics. BMSDM comprehensively outperforms the competing methods in multi-objective decision-making scenarios. Our proposed approach represents a significant leap forward in creating an intelligent autonomous platform capable of novel material discovery.
Beams of radioactive heavy ions allow researchers to study rare and unstable atomic nuclei, shedding light into the internal structure of exotic nuclei and on how chemical elements are formed in stars. However, the extraction and transport of radioactive beams rely on time-consuming expert-driven tuning methods, where hundreds of parameters are manually optimized. Here, we introduce a system that employs Artificial Intelligence (AI), specifically utilizing Bayesian Optimization, to assist in the transport process of radioactive beams. We apply our methodology to real-life scenarios showing advantages when compared with standard tuning methods. This AI-assisted approach can be extended to other radioactive beam facilities around the world to improve operational efficiency and enhance scientific output.
Bayesian optimization based on Gaussian process upper confidence bound (GP-UCB) has a theoretical guarantee for optimizing black-box functions. Black-box functions often have input uncertainty, but even in this case, GP-UCB can be extended to optimize evaluation measures called robustness measures. However, GP-UCB-based methods for robustness measures include a trade-off parameter $\beta$, which must be excessively large to achieve theoretical validity, just like the original GP-UCB. In this study, we propose a new method called randomized robustness measure GP-UCB (RRGP-UCB), which samples the trade-off parameter $\beta$ from a probability distribution based on a chi-squared distribution and avoids explicitly specifying $\beta$. The expected value of $\beta$ is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected value of regret based on the optimal solution and estimated solutions. Finally, we demonstrate the usefulness of the proposed method through numerical experiments.
Bayesian optimization (BO) is a leading method for optimizing expensive black-box optimization and has been successfully applied across various scenarios. However, BO suffers from the curse of dimensionality, making it challenging to scale to high-dimensional problems. Existing work has adopted a variable selection strategy to select and optimize only a subset of variables iteratively. Although this approach can mitigate the high-dimensional challenge in BO, it still leads to sample inefficiency. To address this issue, we introduce a novel method that identifies important variables by estimating the length scales of Gaussian process kernels. Next, we construct an effective search region consisting of multiple subspaces and optimize the acquisition function within this region, focusing on only the important variables. We demonstrate that our proposed method achieves cumulative regret with a sublinear growth rate in the worst case while maintaining computational efficiency. Experiments on high-dimensional synthetic functions and real-world problems show that our method achieves state-of-the-art performance.
In this paper, we describe the migration of a homebrewed C++ search engine to OpenSearch, aimed at preserving and improving search performance with minimal impact on business metrics. To facilitate the migration, we froze our job corpus and executed queries in low inventory locations to capture a representative mixture of high- and low-quality search results. These query-job pairs were labeled by crowd-sourced annotators using a custom rubric designed to reflect relevance and user satisfaction. Leveraging Bayesian optimization, we fine-tuned a new retrieval algorithm on OpenSearch, replicating key components of the original engine's logic while introducing new functionality where necessary. Through extensive online testing, we demonstrated that the new system performed on par with the original, showing improvements in specific engagement metrics, with negligible effects on revenue.
Bayesian optimization (BO) has recently become more prevalent in protein engineering applications and hence has become a fruitful target of benchmarks. However, current BO comparisons often overlook real-world considerations like risk and cost constraints. In this work, we compare 72 model combinations of encodings, surrogate models, and acquisition functions on 11 protein binder fitness landscapes, specifically from this perspective. Drawing from the portfolio optimization literature, we adopt metrics to quantify the cold-start performance relative to a random baseline, to assess the risk of an optimization campaign, and to calculate the overall budget required to reach a fitness threshold. Our results suggest the existence of Pareto-optimal models on the risk-performance axis, the shift of this preference depending on the landscape explored, and the robust correlation between landscape properties such as epistasis with the average and worst-case model performance. They also highlight that rigorous model selection requires substantial computational and statistical efforts.
The ability to discover meaningful, accurate, and concise mathematical equations that describe datasets is valuable across various domains. Equations offer explicit relationships between variables, enabling deeper insights into underlying data patterns. Most existing equation discovery methods rely on genetic programming, which iteratively searches the equation space but is often slow and prone to overfitting. By representing equations as directed acyclic graphs, we leverage the use of graph neural networks to learn the underlying semantics of equations, and generate new, previously unseen equations. Although graph generative models have been shown to be successful in discovering new types of graphs in many fields, there application in discovering equations remains largely unexplored. In this work, we propose Graph-EQ, a deep graph generative model designed for efficient equation discovery. Graph-EQ uses a conditional variational autoencoder (CVAE) to learn a rich latent representation of the equation space by training it on a large corpus of equations in an unsupervised manner. Instead of directly searching the equation space, we employ Bayesian optimization to efficiently explore this learned latent space. We show that the encoder-decoder architecture of Graph-Eq is able to accurately reconstruct input equations. Moreover, we show that the learned latent representation can be sampled and decoded into valid equations, including new and previously unseen equations in the training data. Finally, we assess Graph-Eq's ability to discover equations that best fit a dataset by exploring the latent space using Bayesian optimization. Latent space exploration is done on 20 dataset with known ground-truth equations, and Graph-Eq is shown to successfully discover the grountruth equation in the majority of datasets.
Careful curation of data sources can significantly improve the performance of LLM pre-training, but predominant approaches rely heavily on intuition or costly trial-and-error, making them difficult to generalize across different data domains and downstream tasks. Although scaling laws can provide a principled and general approach for data curation, standard deterministic extrapolation from small-scale experiments to larger scales requires strong assumptions on the reliability of such extrapolation, whose brittleness has been highlighted in prior works. In this paper, we introduce a $\textit{probabilistic extrapolation framework}$ for data mixture optimization that avoids rigid assumptions and explicitly models the uncertainty in performance across decision variables. We formulate data curation as a sequential decision-making problem$\unicode{x2013}$multi-fidelity, multi-scale Bayesian optimization$\unicode{x2013}$where $\{$data mixtures, model scale, training steps$\}$ are adaptively selected to balance training cost and potential information gain. Our framework naturally gives rise to algorithm prototypes that leverage noisy information from inexpensive experiments to systematically inform costly training decisions. To accelerate methodological progress, we build a simulator based on 472 language model pre-training runs with varying data compositions from the SlimPajama dataset. We observe that even simple kernels and acquisition functions can enable principled decisions across training models from 20M to 1B parameters and achieve $\textbf{2.6x}$ and $\textbf{3.3x}$ speedups compared to multi-fidelity BO and random search baselines. Taken together, our framework underscores potential efficiency gains achievable by developing principled and transferable data mixture optimization methods.
Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal graph, which is a limitation in many real-world scenarios where such graphs are unknown. To address this, we propose a new method for the CBO framework that operates without prior knowledge of the causal graph. Consistent with causal bandit theory, we demonstrate through theoretical analysis and that focusing on the direct causal parents of the target variable is sufficient for optimization, and provide empirical validation in the context of CBO. Furthermore we introduce a new method that learns a Bayesian posterior over the direct parents of the target variable. This allows us to optimize the outcome variable while simultaneously learning the causal structure. Our contributions include a derivation of the closed-form posterior distribution for the linear case. In the nonlinear case where the posterior is not tractable, we present a Gaussian Process (GP) approximation that still enables CBO by inferring the parents of the outcome variable. The proposed method performs competitively with existing benchmarks and scales well to larger graphs, making it a practical tool for real-world applications where causal information is incomplete.
Accelerating the discovery and manufacturing of advanced materials with specific properties is a critical yet formidable challenge due to vast search space, high costs of experiments, and time-intensive nature of material characterization. In recent years, active learning, where a surrogate machine learning (ML) model mimics the scientific discovery process of a human scientist, has emerged as a promising approach to address these challenges by guiding experimentation toward high-value outcomes with a limited budget. Among the diverse active learning philosophies, the concept of surprise (capturing the divergence between expected and observed outcomes) has demonstrated significant potential to drive experimental trials and refine predictive models. Scientific discovery often stems from surprise thereby making it a natural driver to guide the search process. Despite its promise, prior studies leveraging surprise metrics such as Shannon and Bayesian surprise lack mechanisms to account for prior confidence, leading to excessive exploration of uncertain regions that may not yield useful information. To address this, we propose the Confidence-Adjusted Surprise Measure for Active Resourceful Trials (CA-SMART), a novel Bayesian active learning framework tailored for optimizing data-driven experimentation. On a high level, CA-SMART incorporates Confidence-Adjusted Surprise (CAS) to dynamically balance exploration and exploitation by amplifying surprises in regions where the model is more certain while discounting them in highly uncertain areas. We evaluated CA-SMART on two benchmark functions (Six-Hump Camelback and Griewank) and in predicting the fatigue strength of steel. The results demonstrate superior accuracy and efficiency compared to traditional surprise metrics, standard Bayesian Optimization (BO) acquisition functions and conventional ML methods.
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.
Ensuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433\% to 0.0163\%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82\% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3\%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.
Safety is of paramount importance in control systems to avoid costly risks and catastrophic damages. The control barrier function (CBF) method, a promising solution for safety-critical control, poses a new challenge of enhancing control performance due to its direct modification of original control design and the introduction of uncalibrated parameters. In this work, we shed light on the crucial role of configurable parameters in the CBF method for performance enhancement with a systematical categorization. Based on that, we propose a novel framework combining the CBF method with Bayesian optimization (BO) to optimize the safe control performance. Considering feasibility/safety-critical constraints, we develop a safe version of BO using the barrier-based interior method to efficiently search for promising feasible configurable parameters. Furthermore, we provide theoretical criteria of our framework regarding safety and optimality. An essential advantage of our framework lies in that it can work in model-agnostic environments, leaving sufficient flexibility in designing objective and constraint functions. Finally, simulation experiments on swing-up control and high-fidelity adaptive cruise control are conducted to demonstrate the effectiveness of our framework.
The rapid advancement of machine learning and artificial intelligence (AI)-driven techniques is revolutionizing materials discovery, property prediction, and material design by minimizing human intervention and accelerating scientific progress. This review provides a comprehensive overview of smart, machine learning (ML)-driven approaches, emphasizing their role in predicting material properties, discovering novel compounds, and optimizing material structures. Key methodologies ranging from deep learning, graph neural networks, and Bayesian optimization to automated generative models, such as generative adversarial networks (GANs) and variational autoencoders (VAEs) enable the autonomous design of materials with tailored functionalities. By leveraging AutoML frameworks (e.g., AutoGluon, TPOT, and H2O.ai), researchers can automate the model selection, hyperparameter tuning, and feature engineering, significantly improving the efficiency of materials informatics. Furthermore, the integration of AI-driven robotic laboratories and high-throughput computing has established a fully automated pipeline for rapid synthesis and experimental validation, drastically reducing the time and cost of material discovery. This review highlights real-world applications of automated ML-driven approaches in predicting mechanical, thermal, electrical, and optical properties of materials, demonstrating successful cases in superconductors, catalysts, photovoltaics, and energy storage systems. We also address key challenges, such as data quality, interpretability, and the integration of AutoML with quantum computing, which are essential for future advancements. Ultimately, the synergy between AI, automated experimentation, and computational modeling transforms the way the materials are discovered, optimized, and designed, paving the way for next-generation innovations in energy, electronics, and nanotechnology.
Decarbonization of the transport sector sets increasingly strict demands to maximize thermal efficiency and minimize greenhouse gas emissions of Internal Combustion Engines. This has led to complex engines with a surge in the number of corresponding tunable parameters in actuator set points and control settings. Automated calibration is therefore essential to keep development time and costs at acceptable levels. In this work, an innovative self-learning calibration method is presented based on in-cylinder pressure curve shaping. This method combines Principal Component Decomposition with constrained Bayesian Optimization. To realize maximal thermal engine efficiency, the optimization problem aims at minimizing the difference between the actual in-cylinder pressure curve and an Idealized Thermodynamic Cycle. By continuously updating a Gaussian Process Regression model of the pressure's Principal Components weights using measurements of the actual operating conditions, the mean in-cylinder pressure curve as well as its uncertainty bounds are learned. This information drives the optimization of calibration parameters, which are automatically adapted while dealing with the risks and uncertainties associated with operational safety and combustion stability. This data-driven method does not require prior knowledge of the system. The proposed method is successfully demonstrated in simulation using a Reactivity Controlled Compression Ignition engine model. The difference between the Gross Indicated Efficiency of the optimal solution found and the true optimum is 0.017%. For this complex engine, the optimal solution was found after 64.4s, which is relatively fast compared to conventional calibration methods.
Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evaluations of the expensive-to-evaluate objective function. The proposed algorithm's competitive performance is demonstrated through practical examples.
Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective function is known and differentiable. Existing work in black-box settings with unknown objectives that can only be sampled either assumes convexity-concavity in the objective to simplify the problem or operates with noisy gradient estimators. In contrast, we introduce a framework inspired by Bayesian optimization which utilizes Gaussian processes to model the unknown (potentially nonconvex-nonconcave) objective and requires only zeroth-order samples. Our approach frames the saddle point optimization problem as a two-level process which can flexibly integrate existing and novel approaches to this problem. The upper level of our framework produces a model of the objective function by sampling in promising locations, and the lower level of our framework uses the existing model to frame and solve a general-sum game to identify locations to sample. This lower level procedure can be designed in complementary ways, and we demonstrate the flexibility of our approach by introducing variants which appropriately trade off between factors like runtime, the cost of function evaluations, and the number of available initial samples. We experimentally demonstrate these algorithms on synthetic and realistic datasets in black-box nonconvex-nonconcave settings, showcasing their ability to efficiently locate local saddle points in these contexts.
Automatic robotic facial expression generation is crucial for human-robot interaction, as handcrafted methods based on fixed joint configurations often yield rigid and unnatural behaviors. Although recent automated techniques reduce the need for manual tuning, they tend to fall short by not adequately bridging the gap between human preferences and model predictions-resulting in a deficiency of nuanced and realistic expressions due to limited degrees of freedom and insufficient perceptual integration. In this work, we propose a novel learning-to-rank framework that leverages human feedback to address this discrepancy and enhanced the expressiveness of robotic faces. Specifically, we conduct pairwise comparison annotations to collect human preference data and develop the Human Affective Pairwise Impressions (HAPI) model, a Siamese RankNet-based approach that refines expression evaluation. Results obtained via Bayesian Optimization and online expression survey on a 35-DOF android platform demonstrate that our approach produces significantly more realistic and socially resonant expressions of Anger, Happiness, and Surprise than those generated by baseline and expert-designed methods. This confirms that our framework effectively bridges the gap between human preferences and model predictions while robustly aligning robotic expression generation with human affective responses.
Despite decades of advancements in automated ligand screening, large-scale drug discovery remains resource-intensive and requires post-processing hit selection, a step where chemists manually select a few promising molecules based on their chemical intuition. This creates a major bottleneck in the virtual screening process for drug discovery, demanding experts to repeatedly balance complex trade-offs among drug properties across a vast pool of candidates. To improve the efficiency and reliability of this process, we propose a novel human-centered framework named CheapVS that allows chemists to guide the ligand selection process by providing preferences regarding the trade-offs between drug properties via pairwise comparison. Our framework combines preferential multi-objective Bayesian optimization with a docking model for measuring binding affinity to capture human chemical intuition for improving hit identification. Specifically, on a library of 100K chemical candidates targeting EGFR and DRD2, CheapVS outperforms state-of-the-art screening methods in identifying drugs within a limited computational budget. Notably, our method can recover up to 16/37 EGFR and 37/58 DRD2 known drugs while screening only 6% of the library, showcasing its potential to significantly advance drug discovery.