Manipulating the shape of a liquid droplet is essential for a wide range of applications in medicine and industry. However, existing methods are typically limited to generating simple shapes, such as ellipses, or rely on predefined templates. Although recent approaches have demonstrated more complex geometries, they remain constrained by limited adaptability and lack of real-time control. Here, we introduce a data-efficient method that enables real-time, programmable shaping of nonmagnetic liquid droplets into diverse target forms at the air-ferrofluid interface using Bayesian optimization. The droplet can adopt either convex or concave shapes depending on the actuation of the surrounding electromagnets. Bayesian optimization determines the optimal magnetic flux density for shaping the liquid droplet into a desired target shape. Our method enables automatic shaping into various triangular and rectangular shapes with a maximum shape error of 0.81 mm, as well as into letter-like patterns. To the best of our knowledge, this is the first demonstration of real-time, automatic shaping of nonmagnetic liquid droplets into desired target shapes using magnetic fields or other external energy fields.
Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically demonstrated that the Gaussian Process fitting procedure at its core could be its most relevant weakness. Fitting a Gaussian Process means tuning its kernel's hyperparameters to a set of observations, but the common Maximum Likelihood Estimation technique, usually appropriate for learning tasks, has shown different criticalities in Bayesian Optimization, making theoretical analysis of this algorithm an open challenge. Exploiting the analogy between Gaussian Processes and Gaussian Distributions, we present a new approach which uses a prefixed set of hyperparameters values to fit as many Gaussian Processes and then combines them into a unique model as a Wasserstein Barycenter of Gaussian Processes. We considered both "easy" test problems and others known to undermine the \textit{vanilla} Bayesian Optimization algorithm. The new method, namely Wasserstein Barycenter Gausssian Process based Bayesian Optimization (WBGP-BO), resulted promising and able to converge to the optimum, contrary to vanilla Bayesian Optimization, also on the most "tricky" test problems.
Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying black-box objective function that may be noisy and expensive to evaluate. Is it possible for the instantaneous regret of a TVBO algorithm to vanish asymptotically, and if so, when? We answer this question of great theoretical importance by providing algorithm-independent lower regret bounds and upper regret bounds for TVBO algorithms, from which we derive sufficient conditions for a TVBO algorithm to have the no-regret property. Our analysis covers all major classes of stationary kernel functions.
The performance of an LLM depends heavily on the relevance of its training data to the downstream evaluation task. However, in practice, the data involved in an unseen evaluation task is often unknown (e.g., conversations between an LLM and a user are end-to-end encrypted). Hence, it is unclear what data are relevant for fine-tuning the LLM to maximize its performance on the specific unseen evaluation task. Instead, one can only deploy the LLM on the unseen task to gather multiple rounds of feedback on how well the model performs (e.g., user ratings). This novel setting offers a refreshing perspective towards optimizing training data mixtures via feedback from an unseen evaluation task, which prior data mixing and selection works do not consider. Our paper presents DUET, a novel global-to-local algorithm that interleaves influence function as a data selection method with Bayesian optimization to optimize data mixture via feedback from a specific unseen evaluation task. By analyzing DUET's cumulative regret, we theoretically show that DUET converges to the optimal training data mixture for an unseen task even without any data knowledge of the task. Finally, our experiments across a variety of language tasks demonstrate that DUET outperforms existing data selection and mixing methods in the unseen-task setting.
Many real-world scientific and industrial applications require the optimization of expensive black-box functions. Bayesian Optimization (BO) provides an effective framework for such problems. However, traditional BO methods are prone to get trapped in local optima and often lack interpretable insights. To address this issue, this paper designs Reasoning BO, a novel framework that leverages reasoning models to guide the sampling process in BO while incorporating multi-agent systems and knowledge graphs for online knowledge accumulation. By integrating the reasoning and contextual understanding capabilities of Large Language Models (LLMs), we can provide strong guidance to enhance the BO process. As the optimization progresses, Reasoning BO provides real-time sampling recommendations along with critical insights grounded in plausible scientific theories, aiding in the discovery of superior solutions within the search space. We systematically evaluate our approach across 10 diverse tasks encompassing synthetic mathematical functions and complex real-world applications. The framework demonstrates its capability to progressively refine sampling strategies through real-time insights and hypothesis evolution, effectively identifying higher-performing regions of the search space for focused exploration. This process highlights the powerful reasoning and context-learning abilities of LLMs in optimization scenarios. For example, in the Direct Arylation task, our method increased the yield to 60.7%, whereas traditional BO achieved only a 25.2% yield. Furthermore, our investigation reveals that smaller LLMs, when fine-tuned through reinforcement learning, can attain comparable performance to their larger counterparts. This enhanced reasoning capability paves the way for more efficient automated scientific experimentation while maintaining computational feasibility.
As climate change increases the threat of weather-related disasters, research on weather control is gaining importance. The objective of weather control is to mitigate disaster risks by administering interventions with optimal timing, location, and intensity. However, the optimization process is highly challenging due to the vast scale and complexity of weather phenomena, which introduces two major challenges. First, obtaining accurate gradient information for optimization is difficult. In addition, numerical weather prediction (NWP) models demand enormous computational resources, necessitating parameter optimization with minimal function evaluations. To address these challenges, this study proposes a method for designing weather interventions based on black-box optimization, which enables efficient exploration without requiring gradient information. The proposed method is evaluated in two distinct control scenarios: one-shot initial value intervention and sequential intervention based on model predictive control. Furthermore, a comparative analysis is conducted among four representative black-box optimization methods in terms of total rainfall reduction. Experimental results show that Bayesian optimization achieves higher control effectiveness than the others, particularly in high-dimensional search spaces. These findings suggest that Bayesian optimization is a highly effective approach for weather intervention computation.
Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing for different models to address each part, making them well-suited for problems with inherent hierarchical structure. However, typical H-GP models do not fully take advantage of this structure, only sending information up or down the hierarchy. This one-way coupling limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), an efficient H-GP framework that establishes bidirectional information exchange between parent and child models in H-GPs for online training. BIF retains the modular structure of hierarchical models - the parent combines subtask knowledge from children GPs - while introducing top-down feedback to continually refine children models during online learning. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. BIF outperforms conventional H-GP Bayesian Optimization methods, achieving up to 85% and 5x higher $R^2$ scores for the parent and children respectively, on synthetic and real-world neurostimulation optimization tasks.
Preferential Bayesian optimization (PBO) is a variant of Bayesian optimization that observes relative preferences (e.g., pairwise comparisons) instead of direct objective values, making it especially suitable for human-in-the-loop scenarios. However, real-world optimization tasks often involve inequality constraints, which existing PBO methods have not yet addressed. To fill this gap, we propose constrained preferential Bayesian optimization (CPBO), an extension of PBO that incorporates inequality constraints for the first time. Specifically, we present a novel acquisition function for this purpose. Our technical evaluation shows that our CPBO method successfully identifies optimal solutions by focusing on exploring feasible regions. As a practical application, we also present a designer-in-the-loop system for banner ad design using CPBO, where the objective is the designer's subjective preference, and the constraint ensures a target predicted click-through rate. We conducted a user study with professional ad designers, demonstrating the potential benefits of our approach in guiding creative design under real-world constraints.
Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints, and one of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of the expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\mathcal{O} \left(t^{-\frac{1}{2}}\log^{\frac{d+1}{2}}(t) \right) \ \text{and }\ \mathcal{O}\left(t^{\frac{-\nu}{2\nu+d}} \log^{\frac{\nu}{2\nu+d}}(t)\right)$ for the commonly used squared exponential and Mat\'{e}rn kernels, respectively. Second, we show that when $f$ and $c$ are assumed to be sampled from Gaussian processes (GPs), CEI achieves the same convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.
Bayesian Optimization (BO) in high-dimensional spaces remains fundamentally limited by the curse of dimensionality and the rigidity of global low-dimensional assumptions. While Random EMbedding Bayesian Optimization (REMBO) mitigates this via linear projections into low-dimensional subspaces, it typically assumes a single global embedding and a stationary objective. In this work, we introduce Self-Adaptive embedding REMBO (SA-REMBO), a novel framework that generalizes REMBO to support multiple random Gaussian embeddings, each capturing a different local subspace structure of the high-dimensional objective. An index variable governs the embedding choice and is jointly modeled with the latent optimization variable via a product kernel in a Gaussian Process surrogate. This enables the optimizer to adaptively select embeddings conditioned on location, effectively capturing locally varying effective dimensionality, nonstationarity, and heteroscedasticity in the objective landscape. We theoretically analyze the expressiveness and stability of the index-conditioned product kernel and empirically demonstrate the advantage of our method across synthetic and real-world high-dimensional benchmarks, where traditional REMBO and other low-rank BO methods fail. Our results establish SA-REMBO as a powerful and flexible extension for scalable BO in complex, structured design spaces.
Epilepsy is a prevalent neurological disease with millions of patients worldwide. Many patients have turned to alternative medicine due to the limited efficacy and side effects of conventional antiepileptic drugs. In this study, we developed a computational approach to optimize herbal epilepsy treatment through AI-driven analysis of global natural products and statistically validated randomized controlled trials (RCTs). Our intelligent prescription system combines machine learning (ML) algorithms for herb-efficacy characterization, Bayesian optimization for personalized dosing, and meta-analysis of RCTs for evidence-based recommendations. The system analyzed 1,872 natural compounds from traditional Chinese medicine (TCM), Ayurveda, and ethnopharmacological databases, integrating their bioactive properties with clinical outcomes from 48 RCTs covering 48 epilepsy conditions (n=5,216). Using LASSO regression and SHAP value analysis, we identified 17 high-efficacy herbs (e.g., Gastrodia elata [using \'e for accented characters], Withania somnifera), showing significant seizure reduction (p$<$0.01, Cohen's d=0.89) with statistical significance confirmed by multiple testing (p$<$0.001). A randomized double-blind validation trial (n=120) demonstrated 28.5\% greater seizure frequency reduction with AI-optimized herbal prescriptions compared to conventional protocols (95\% CI: 18.7-37.3\%, p=0.003).
This case study applies a phased hyperparameter optimization process to compare multitask natural language model variants that utilize multiphase learning rate scheduling and optimizer parameter grouping. We employ short, Bayesian optimization sessions that leverage multi-fidelity, hyperparameter space pruning, progressive halving, and a degree of human guidance. We utilize the Optuna TPE sampler and Hyperband pruner, as well as the Scikit-Learn Gaussian process minimization. Initially, we use efficient low-fidelity sprints to prune the hyperparameter space. Subsequent sprints progressively increase their model fidelity and employ hyperband pruning for efficiency. A second aspect of our approach is using a meta-learner to tune threshold values to resolve classification probabilities during inference. We demonstrate our method on a collection of variants of the 2021 Joint Entity and Relation Extraction model proposed by Eberts and Ulges.
Bayesian inference has many advantages in decision making of agents (e.g. robotics/simulative agent) over a regular data-driven black-box neural network: Data-efficiency, generalization, interpretability, and safety where these advantages benefit directly/indirectly from the uncertainty quantification of Bayesian inference. However, there are few comprehensive reviews to summarize the progress of Bayesian inference on reinforcement learning (RL) for decision making to give researchers a systematic understanding. This paper focuses on combining Bayesian inference with RL that nowadays is an important approach in agent decision making. To be exact, this paper discusses the following five topics: 1) Bayesian methods that have potential for agent decision making. First basic Bayesian methods and models (Bayesian rule, Bayesian learning, and Bayesian conjugate models) are discussed followed by variational inference, Bayesian optimization, Bayesian deep learning, Bayesian active learning, Bayesian generative models, Bayesian meta-learning, and lifelong Bayesian learning. 2) Classical combinations of Bayesian methods with model-based RL (with approximation methods), model-free RL, and inverse RL. 3) Latest combinations of potential Bayesian methods with RL. 4) Analytical comparisons of methods that combine Bayesian methods with RL with respect to data-efficiency, generalization, interpretability, and safety. 5) In-depth discussions in six complex problem variants of RL, including unknown reward, partial-observability, multi-agent, multi-task, non-linear non-Gaussian, and hierarchical RL problems and the summary of how Bayesian methods work in the data collection, data processing and policy learning stages of RL to pave the way for better agent decision-making strategies.
We developed an interpretability informed Bayesian optimization framework to optimize underwater acoustic coatings based on polyurethane elastomers with embedded metamaterial features. A data driven model was employed to analyze the relationship between acoustic performance, specifically sound absorption and the corresponding design variables. By leveraging SHapley Additive exPlanations (SHAP), a machine learning interpretability tool, we identified the key parameters influencing the objective function and gained insights into how these parameters affect sound absorption. The insights derived from the SHAP analysis were subsequently used to automatically refine the bounds of the optimization problem automatically, enabling a more targeted and efficient exploration of the design space. The proposed approach was applied to two polyurethane materials with distinct hardness levels, resulting in improved optimal solutions compared to those obtained without SHAP-informed guidance. Notably, these enhancements were achieved without increasing the number of simulation iterations. Our findings demonstrate the potential of SHAP to streamline optimization processes by uncovering hidden parameter relationships and guiding the search toward promising regions of the design space. This work underscores the effectiveness of combining interpretability techniques with Bayesian optimization for the efficient and cost-effective design of underwater acoustic metamaterials under strict computational constraints and can be generalized towards other materials and engineering optimization problems.
This paper presented a novel device-free localization (DFL) framework based on distributed antenna networks (DANs), targeting integrated sensing and communication (ISAC) in future 6G radio access networks (RANs). In the proposed approach, radio tomographic imaging (RTI) leverages the spatial and temporal diversity of multi-link multiple-input multiple-output (MIMO) channels in DANs to improve localization accuracy. Furthermore, a prototype system was developed using software-defined radios (SDRs) operating in the sub-6 GHz band, and comprehensive evaluations were conducted under indoor conditions involving varying node densities and target types. The results demonstrate that the framework achieves sub-meter localization accuracy in most scenarios and maintains robust performance under complex multipath environments. In addition, the use of Bayesian optimization to fine-tune key parameters, such as sparsity and path thickness, led to significant improvements in image reconstruction quality and target estimation accuracy. These results demonstrate the feasibility and effectiveness of DAN-based DFL systems for accurate, robust, and scalable localization.
Artificial intelligence (AI) techniques are transforming analog circuit design by automating device-level tuning and enabling system-level co-optimization. This paper integrates two approaches: (1) AI-assisted transistor sizing using Multi-Objective Bayesian Optimization (MOBO) for direct circuit parameter optimization, demonstrated on a linearly tunable transconductor; and (2) AI-integrated circuit transfer function modeling for system-level optimization in a keyword spotting (KWS) application, demonstrated by optimizing an analog bandpass filter within a machine learning training loop. The combined insights highlight how AI can improve analog performance, reduce design iteration effort, and jointly optimize analog components and application-level metrics.
Objective: To develop and evaluate a scalable methodology for harmonizing inconsistent units in large-scale clinical datasets, addressing a key barrier to data interoperability. Materials and Methods: We designed a novel unit harmonization system combining BM25, sentence embeddings, Bayesian optimization, and a bidirectional transformer based binary classifier for retrieving and matching laboratory test entries. The system was evaluated using the Optum Clinformatics Datamart dataset (7.5 billion entries). We implemented a multi-stage pipeline: filtering, identification, harmonization proposal generation, automated re-ranking, and manual validation. Performance was assessed using Mean Reciprocal Rank (MRR) and other standard information retrieval metrics. Results: Our hybrid retrieval approach combining BM25 and sentence embeddings (MRR: 0.8833) significantly outperformed both lexical-only (MRR: 0.7985) and embedding-only (MRR: 0.5277) approaches. The transformer-based reranker further improved performance (absolute MRR improvement: 0.10), bringing the final system MRR to 0.9833. The system achieved 83.39\% precision at rank 1 and 94.66\% recall at rank 5. Discussion: The hybrid architecture effectively leverages the complementary strengths of lexical and semantic approaches. The reranker addresses cases where initial retrieval components make errors due to complex semantic relationships in medical terminology. Conclusion: Our framework provides an efficient, scalable solution for unit harmonization in clinical datasets, reducing manual effort while improving accuracy. Once harmonized, data can be reused seamlessly in different analyses, ensuring consistency across healthcare systems and enabling more reliable multi-institutional studies and meta-analyses.
While Retrieval Augmented Generation (RAG) has emerged as a popular technique for improving Large Language Model (LLM) systems, it introduces a large number of choices, parameters and hyperparameters that must be made or tuned. This includes the LLM, embedding, and ranker models themselves, as well as hyperparameters governing individual RAG components. Yet, collectively optimizing the entire configuration in a RAG or LLM system remains under-explored - especially in multi-objective settings - due to intractably large solution spaces, noisy objective evaluations, and the high cost of evaluations. In this work, we introduce the first approach for multi-objective parameter optimization of cost, latency, safety and alignment over entire LLM and RAG systems. We find that Bayesian optimization methods significantly outperform baseline approaches, obtaining a superior Pareto front on two new RAG benchmark tasks. We conclude our work with important considerations for practitioners who are designing multi-objective RAG systems, highlighting nuances such as how optimal configurations may not generalize across tasks and objectives.
The fine-tuning of pre-trained language models has resulted in the widespread availability of task-specific models. Model merging offers an efficient way to create multi-task models by combining these fine-tuned models at the parameter level, without the need for training data or joint training on multiple datasets. Existing merging approaches typically involve scaling the parameters model-wise or integrating parameter importance parameter-wise. Both approaches exhibit their own weaknesses, leading to a notable performance gap compared to multi-task fine-tuning. In this paper, we unify these seemingly distinct strategies into a more general merging framework, and introduce Dynamic Fisher-weighted Merging (DF-Merge). Specifically, candidate models are associated with a set of coefficients that linearly scale their fine-tuned parameters. Bayesian optimization is applied to dynamically adjust these coefficients, aiming to maximize overall performance on validation sets. Each iteration of this process integrates parameter importance based on the Fisher information conditioned by the coefficients. Experimental results show that DF-Merge outperforms strong baselines across models of different sizes and a variety of tasks. Our analysis shows that the effectiveness of DF-Merge arises from the unified view of merging and that near-optimal performance is achievable in a few iterations, even with minimal validation data.
We develop and analyze a method for stochastic simulation optimization relying on Gaussian process models within a trust-region framework. We are interested in the case when the variance of the objective function is large. We propose to rely on replication and local modeling to cope with this high-throughput regime, where the number of evaluations may become large to get accurate results while still keeping good performance. We propose several schemes to encourage replication, from the choice of the acquisition function to setup evaluation costs. Compared with existing methods, our results indicate good scaling, in terms of both accuracy (several orders of magnitude better than existing methods) and speed (taking into account evaluation costs).