Bayesian Optimization

Optimizing industrial process flowsheets is often computationally prohibitive due to the high cost of rigorous simulations and the curse of dimensionality inherent in complex design spaces. To address these challenges, we present a reduced-space multi-fidelity Bayesian optimization (RS-MFBO) framework designed for high-dimensional, expensive black-box functions. The approach integrates Global Sensitivity Analysis (GSA) for dimensionality reduction with a fidelity-augmented Gaussian process that captures correlations between low-cost approximations and expensive high-fidelity evaluations. A cost-aware acquisition strategy, augmented with cooldown and promotion mechanisms, adaptively guides the allocation of samples across fidelities. The framework is validated on two distinct industrial process simulators: a plasmid DNA bioprocess in SuperPro Designer and a green fuel synthesis plant in Aspen HYSYS. Results across diverse economic and physical objectives demonstrate that the proposed method substantially reduces the number of high-fidelity simulator evaluations while maintaining competitive optimization performance compared to single-fidelity baselines. These results highlight RS-MFBO as a scalable, simulator-agnostic approach for cost-constrained black-box optimization.

Bayesian optimisation (BO) typically relies on a single global Gaussian process (GP) model as its surrogate model. However, GP regression has cubic computational complexity in the number of training data points, limiting its applicability to large-scale optimisation problems. The product-of-experts Gaussian process model with uncertainty calibration (GP-pro-c) mitigates this limitation by combining multiple local GP experts, enabling improved uncertainty quantification, reduced computational cost, and preservation of global correlations. Despite these desirable properties, the use of GP-pro-c in BO has not been thoroughly studied. This paper introduces BO-pro-c, a Bayesian optimisation algorithm that uses GP-pro-c as its surrogate model, and evaluate its performance across a diverse range of BO settings. Experimental results suggest that BO-pro-c maintains competitive optimisation performance while achieving a 0.9% reduction in simple regret and a 39.4% reduction in computational overhead relative to a BO algorithm based on a single global GP model.

In the past decade, Bayesian optimization (BO) has emerged as a powerful and adaptable framework for automatic controller tuning and robot learning. This article offers a comprehensive overview of the state-of-the-art in BO, designed to support both researchers and practitioners in understanding recent advancements, practical applications, and future research directions. We begin by adopting a practitioner's perspective, illustrating how to effectively set up BO through a representative controller tuning example. We position BO within the broader context of learning paradigms, ranging from deep reinforcement learning to data-driven control, and highlight scenarios where BO is most advantageous. Next, we discuss the diverse range of BO methods that have been developed to tackle complex problems and specific applications. This article provides a unified perspective on the current landscape of BO, emphasizing its relevance to control systems and robotics, and it highlights future prospects by identifying key research challenges and promising avenues for advancing BO in the field. This includes addressing a significant gap in the BO landscape: the lack of standardized benchmark problems specifically for control-related applications. To foster future research and ensure rigorous evaluation, we start an effort towards a lightweight benchmark suite for control engineering and robotics. We also present metrics and best practices to facilitate direct comparisons between new BO algorithms and established state-of-the-art methods.

Hyphenation patterns remain a compact and widely deployed solution for word breaking in typesetting systems, text processors, and web rendering engines, but their generation still depends on manually tuned patgen program parameter profiles. We formulate patgen profile selection as a black-box hyperparameter optimization problem and evaluate Gaussian-process Bayesian optimization for this task. The search objective combines a precision-oriented F_{1/7}-score with an explicit trie size-accuracy trade-off using a normalized trie-size penalty. We evaluate the method on 17 hyphenated word-list datasets covering 14 languages and multiple scripts. Against two strong hand-tuned profiles regenerated from the same 8/10 training split and evaluated on the same 1/10 held-out test split, the GP-optimized profiles improve F_{1/7} on 16 of 17 datasets and reduce trie size on all 17. The median optimized/baseline trie ratio is 0.407. A dataset-level sign test gives p = 1.37e-4; a separate budget-matched comparison on five representative datasets shows that systematic search is competitive and usually improves over the best hand-tuned profile under the fixed comparison objective. The results show that model-based optimization can make pattern generation more reproducible and less dependent on expert trial-and-error while keeping the accuracy-compactness trade-off explicit.

Self-driving laboratories (SDLs) combine automated experimentation with adaptive decision-making to accelerate scientific discovery. Their operation nevertheless often depends on human specialists who translate scientific objectives into executable closed-loop campaigns. Specialists adjust them as data and operating conditions change. Here, we present La Agente 'Optima, an agentic framework that constructs and supervises Bayesian optimization campaigns across computational and experimental systems while maintaining a persistent optimization state. By separating large language model (LLM) reasoning from executed campaigns, 'Optima runs repetitive optimization loops consistently, returns control to the agent only when progress requires interpretation or campaign revision, and keeps every decision auditable. We evaluate 'Optima across ablation studies, five digital discovery tasks, and two physical platforms. Throughout, 'Optima maintained executable campaigns as both the scientific problem and execution environment evolved. In a closed-loop contact angle optimization campaign, 'Optima identified and corrected a mid-run measurement failure, bringing the contact angle from 71.4 to 67.8 degrees, just above the 64-66 degree range. From this result, 'Optima correctly inferred that the target was likely unattainable with the available reagents and recommended changing the formulation. In a five-day multi-objective flow-chemistry campaign, 'Optima increased the yield from 30% to 59% over 23 experiments. Despite substantial inference costs, it cost less and used substantially less starting material than a human-directed campaign, while selecting a more mass-efficient operating point. These results show that LLM-based agents can make rigorous, long-running optimization campaigns accessible to domain scientists without specialist setup, expanding the scope of SDLs.

Gaussian-process Bayesian optimization (GP-BO) excels at black-box optimization of costly functions, e.g., hyperparameter optimization (HPO) and multi-agent system (MAS) design. Convergence-rate guarantees exist for select methods, notably GP upper confidence bound (GP-UCB), but require a fixed kernel. Critically, the kernel encodes how input proximity affects objective value similarity. When raw coordinates poorly match this geometry - as with log-scaled hyperparameters or localized peaks - input warping can greatly improve sample efficiency, yet known GP-UCB proofs require a fixed kernel. We propose Finite-Library Input-Warped Bayesian Optimization (FLIWBO), which selects warps from a finite library of smooth input maps by any history-dependent rule. It adapts the input geometry to accelerate learning while retaining high-probability convergence guarantees under mild hypotheses, with an explicit $\sqrt(N_\varepsilon)$ library-size cost. Controlled diagnostics show that finite-library warping repairs planted geometry mismatches and identify FLIWBO failure cases. Across four repeated benchmarks - warped synthetic objectives, a confidence-fence trap, and Fashion-MNIST HPO - FLIWBO-UCB beats raw-coordinate GP-UCB under misspecified geometry, escapes traps that defeat even oracle-warp expected improvement, and recovers much of the gain from manual log scaling, while leading the tested methods that admit a matching regret guarantee. A 20-dimensional MAS design study further shows feasibility under costly noisy evaluations. Code for experiments is available: https://github.com/edvin-ketabati/bogp-paper-experiments.

The performance of an LLM agent depends on the scaffold around a frozen model. A common way to improve that scaffold is to use a coding agent as an optimizer: it reads current scores and traces and iteratively edits the source, producing a new candidate each round. Each edit is chosen according to a belief about how the environment will respond: what went wrong, and which change should help. That belief is typically implicit. It lives in the coding agent's reasoning on the current call, or remains latent in its parameters, rather than as something written down. Later calls therefore see scores and traces, but they do not use that belief. We introduce Belief-Calibrated Optimization (BCO), a method that writes that belief down as a persistent in-context document and continually revises that document as new candidates are evaluated. The resulting document is a world model: the current account of how the environment responds to edits. Added to an otherwise standard loop, BCO reaches a higher train passrate than a matched control that lacks only the world model, on five benchmarks spanning memory QA, tool-use QA, code-as-action app agents, and terminal agents. The gap remains on every held-out split, which is not used to select the candidate. After a target-model swap, in which the frozen model is replaced and the scaffold is not, the selected BCO scaffold leads on the tasks we test, except where context-window overruns leave it unfinished. An offline ablation then asks whether that gap comes from what the world model says. A fresh predictor given the accumulated document forecasts how the environment will respond more accurately than predictors given either no document or a same-form copy whose content has been falsified. The comparison indicates that the document carries reusable information in its content, not only in its form.

Optimal hyperparameter scaling laws describe how the best hyperparameters for large language model (LLM) training change with model and data scale, enabling practitioners to predict optimal configurations at production scales without expensive large-scale tuning. However, estimating these scaling laws conventionally requires exhaustive grid searches over thousands of training runs, consuming enormous computational resources. We introduce Power-Law Entropy Search (PLES), a computational cost-aware acquisition function built on multi-fidelity Bayesian optimization that efficiently estimates optimal hyperparameter scaling laws through adaptive experimentation. A key innovation in PLES is that it searches for candidates that reduce the overall uncertainty of a scaling law estimate, instead of optimizing a single objective function. At each iteration, PLES selects the candidate configuration that maximally reduces the uncertainty of the scaling law estimates per unit computational cost, naturally favoring informative small-scale experiments. We evaluate PLES on synthetic benchmarks, surrogate models fitted to real LLM training data, and actual LLM pre-training runs. Across all settings, PLES converges to accurate optimal hyperparameter scaling laws using less than one-tenth of the computational budget required by conventional grid search and other baselines.

In this research, a novel framework is proposed for the SOH estimation, which employs a hybrid deep learning architecture of a concatenation of a Convolution Neural Network (CNN) and a Bidirectional Long Short-Term Memory (BiLSTM) Neural Network (NN) with the integration of Bayesian Optimization-based hyperparameter tuning for the network. Three different deep learning architectures are being evaluated: standalone recurrent models, CNN-RNN architectures and CNN-RNN combinations enhanced with intermediate Fully Connected (FC) layers. Among the three, the model with the intermediate FC layers demonstrated the highest predictive accuracy. A comprehensive feature engineering approach combines capacity (Q), voltage (V), Incremental Capacity Analysis (ICA), and Differential Voltage Analysis (DVA), with systematic evaluation of multiple combinations to identify the optimal input representation. To validate the proposed method, three publicly available datasets were utilized, ensuring reproducibility of the results, two from external sources and one developed by the author of this study using a unique experimental setup. The comparison study was performed using the Mean Absolute Error (MAE), the Root Mean Squared Error (RMSE) and the FLoating-point OPerations (FLOPs) as evaluation metrics.

Hyperparameter selection remains a key challenge in Bayesian optimization (BO) and Bayesian active learning (AL), as model misspecification can lead to suboptimal performance, while more accurate fully Bayesian treatments typically rely on computationally expensive MCMC sampling. This paper proposes a unified framework, KENDO (Kernel ENsemble Disagreement-aware Operator), that integrates Ensemble Gaussian Processes (EGP) with disagreement-aware acquisition strategies. The central idea is to replace hyperparameter sampling with a kernel ensemble and adaptive Bayesian weighting, combined with disagreement-aware acquisition strategies. Within this unified framework, we instantiate KENDO-BO for BO and KENDO-AL for Bayesian AL, demonstrating that both arise from a common self-correcting mechanism with task-specific acquisition objectives. We further extend the approach to multi-objective optimization via random scalarization that preserves the single-optimizer conditioning structure. Thorough numerical tests on synthetic and real-world benchmarks across single-objective optimization, multi-objective optimization, and active learning demonstrate that (i) KENDO-BO achieves competitive or superior optimization performance compared to state-of-the-art methods while reducing computational overhead by up to $5\times$ and (ii) KENDO-AL achieves superior predictive calibration over MCMC-based active learning baselines with up to $27\times$ speedup.

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

Bayesian optimization (BO) is a sample-efficient framework for analog circuit topology search, where evaluating each candidate topology can require costly simulation. However, representation-based BO methods typically treat circuit embeddings as fixed after encoder training. This creates a mismatch between representation learning and optimization: embeddings learned to encode or reconstruct circuit structure are not necessarily organized according to the figure of merit (FoM) being optimized. This paper introduces Test-Time Analog Representation Adaptation for Bayesian Optimization (TTARO), an online deep-kernel BO framework that adapts circuit representations throughout the search process. Starting from pretrained circuit embeddings, TTARO jointly learns a nonlinear feature transformation and a Gaussian-process surrogate using the FoM labels of the circuits evaluated so far. Following each new evaluation, TTARO updates the representation and surrogate before selecting the next candidate. We compare TTARO with conventional Gaussian Process-based BO over fixed embeddings and with Deep Kernel Learning (DKL), which learns the representation only from the initial evaluated designs and keeps it fixed throughout the remainder of the search. By continually incorporating newly observed FoM labels into representation learning, TTARO aligns the search space with the optimization objective as BO progresses. In our experiments, TTARO reduces regret AUC by 15.2% on average relative to BO and by 20.7% relative to DKL across 40 encoder/kernel/acquisition settings, outperforming prior art in most settings with reductions as large as 46.7%.

Multi-objective Bayesian optimization (MOBO) is effective in identifying the Pareto fronts for expensive black-box problems. However, most current MOBO approaches are limited to low-dimensional decision space due to its exponential sampling complexity. This paper presents decision variable interaction analysis-based MOBO, ViaMOBO, a generic framework for expensive multi-objective problems with high-dimensional decision space. The key idea of ViaMOBO is that it utilizes a variable interaction analysis model to determine whether the decision space can be completely or partially divided, and then performs local Bayesian optimization in the divided decision subspaces. Through the variable analysis model, it can be derived whether the objectives in black-box problems are separable, partially separable, or non-separable based on the potential independent or interdependent relationships among decision variables without any strong assumptions. We compare ViaMOBO with the state-of-the-art MOBO methods on both synthetic and real-world benchmarks. The experimental results demonstrate that ViaMOBO outperforms other related MOBO baselines in approximating the Pareto front of high-dimensional expensive multi-objective problems.

Gradient-free post-training has emerged as a compelling alternative to gradient-based optimization for large language models (LLMs), but existing approaches remain costly. We ask whether structured search can identify a strong single expert under a modest evaluation budget. Motivated by evidence that useful weight updates lie in low-dimensional subspaces, we apply Bayesian optimization within a random linear embedding of weight space. Our method requires no backpropagation and uses a Gaussian process surrogate to guide candidate evaluations efficiently. Across several reasoning benchmarks with Qwen2.5-Instruct models from 0.5B to 3B parameters, Bayesian optimization using five times less candidate evaluations matches or exceeds RandOpt. These results show that surrogate-guided search can substantially reduce the evaluation cost of gradient-free post-training while producing stronger deployable single experts.

A significant challenge in exoskeleton robotics is the need to dynamically adapt control profiles to individual motion preferences, thereby ensuring both efficient and comfortable assistance. Currently, since user experience can serve as a comprehensive metric for evaluating the effectiveness of assistance, user preference-based optimization methods have been widely studied for parameter tuning. However, the existing methods rely heavily on extensive human-robot online interactions and suffer from slow optimization speed, which not only induces user fatigue but also compromises optimization effectiveness. Therefore, this paper aims to explore an efficient preference-based optimization framework for personalized exoskeleton assistance that can learn optimal parameters with minimal interaction. We propose a preference-based Bayesian optimization (PbBO) approach that can improve sample efficiency by leveraging knowledge about the sampling distribution of candidate sets. For optimizing six control parameters, PbBO can converge to user-preferred parameters with 90.7% validation accuracy via 20 iterations. Moreover, the hierarchical controller is designed to generate personalized torque for different tasks and achieve interaction torque tracking in real time. The results of treadmill and outdoor experiments demonstrate that the optimized parameters can reduce metabolic rate by 14.5%-15.4%, heart rate by 6.3%-7.6%, and muscle activation by 6.7%-31.5% compared to unassisted walking.

Preferential Bayesian optimization (PBO) optimizes objectives accessible only through pairwise user comparisons. The standard approach fits a Gaussian process surrogate for observed pairwise comparisons (PairwiseGP) using the Laplace approximation and selects queries with the Expected Utility of Best Option (EUBO) acquisition function. EUBO queries new candidates at each step, producing pairs that share no candidates with previous queries. Each such pair forms an isolated component in the comparison graph, removing one degree of freedom from the likelihood Hessian and making it rank-deficient. This deficiency is structural and cannot be resolved by changing the surrogate modeling approach. Existing approaches to remedy this issue either waste query budget by forcing comparisons to stay connected, or apply uniform regularization that also perturbs directions already well-constrained by the observed comparisons. We propose KappaSharp that enables a diagonal correction to the Hessian to reduce its condition number, with larger corrections where the prior uncertainty is higher. The correction is only applied in the model fitting step, not query selection. An adaptive variant of KappaSharp is also presented that activates the correction only when the surrogate is confident about recent comparisons, avoiding unnecessary corrections when the problem is well-conditioned. On 11 benchmarks (5--20 dimensions), including a 16-dimensional controller tuning problem in plasma medicine, Adaptive KappaSharp outperforms the standard PBO baseline, with up to +10.9% ($p{=}0.003$).

Advanced materials discovery increasingly relies on machine learning and Bayesian optimization to explore large discrete design spaces under limited evaluation budgets. However, conventional Bayesian optimization (BO) can become inefficient as candidate spaces grow, often evaluating low-value regions before reaching informative areas. We propose an active-learning (AL)-guided adaptive search-space refinement framework combined with multi-objective BO to accelerate materials optimization while preserving Pareto-relevant regions. We evaluate the approach on CH4/N2 separation in covalent-organic frameworks and pressure-vessel design with material-direction stress components and thickness objectives. Results show that the AL-guided refinement reduces the candidate space by approximately half while preserving more than 99 percent of the original hypervolume. The reduced-space strategy improves early convergence and cumulative Pareto-front discovery from the BO, demonstrating efficient large-scale materials optimization across constrained autonomous materials discovery settings.

Black-box optimization is a ubiquitous problem in science and engineering, often dealing with expensive objective functions with cheaper lower-fidelity proxies available. Multi-fidelity Bayesian optimization (MF-BO) is a principled approach to this problem, leveraging correlations across different fidelities when querying the objective. However, for many important MF-BO tasks, the true highest-fidelity function is prohibitively expensive to be part of the optimization loop. Nevertheless, practitioners often have gold standard data (observations of the highest-fidelity function) obtained from previous experiments that might provide information for the current task. For instance, in molecular optimization, chemists often pick the top-$k$ candidate molecules using various computer simulations, and later reveal their true objective function values. In this work, we demonstrate the suboptimality of standard MF-BO algorithms in the real-world scenarios above, even under ideal assumptions. Next, we mitigate this problem by incorporating historical high-fidelity data accompanied by task descriptors---which can be explicitly given or extracted from unstructured metadata. We demonstrate the effectiveness of our methods on synthetic functions, as well as real-world problems in chemistry and hyperparameter optimization.

We consider grey-box optimization problems where the decision variables naturally partition into black-box variables (as arguments to an expensive black-box function) and white-box variables, governed by a set of explicit, closed-form equations that also depend on the output of the black-box function. We exploit this separability through a bilevel reformulation: an outer Bayesian optimization (BO) to optimize the scalar objective as a function of black-box variables alone, while an inner problem solves the white-box subproblem via global optimization. The Gaussian process surrogate used in BO is therefore defined rather than and white-box constraints are satisfied exactly whenever the inner optimizer converges to a feasible point---without penalty functions, chance constraints, or moment approximations. On a suite of 13 benchmark problems, bilevel BO achieves lower regret, with fewer iterations and wall clock time. This advantage is robust to initialization set size, exploration parameters, and inner-solver choice.

Natural disasters frequently inflict severe damage to the built environment, which demands a rapid, reliable, and cost-effective damage assessment for emergency response. However, traditional methods for post-disaster damage assessment often rely on static, labor-intensive data collection strategies that can be prohibitively expensive and struggle to adapt to dynamic post-disaster conditions. In this study, we propose a cost-aware Bayesian optimization framework combined with level-set estimation that continuously guides autonomous data collectors, e.g., an unmanned aerial vehicle (UAV), toward the most informative regions. By dynamically updating damage estimates across different geographic zones, our approach systematically reduces uncertainty while minimizing operational costs. The proposed framework is first validated using a controlled synthetic toy study, demonstrating the agent's ability to efficiently trace damage boundaries, recover the underlying damage map, and rapidly reduce predictive uncertainty. Furthermore, the approach is evaluated using high-fidelity disaster data generated by the Regional Resilience Determination (R2D) software. The results of the algorithm provide accurate and timely damage estimates that support informative and fast emergency response.

Bayesian optimization (BO) relies on a surrogate model and an acquisition function, yet the most suitable choices vary across tasks and optimization stages. Automated Bayesian optimization (AutoBO) addresses this variability by adapting BO components online. However, existing AutoBO methods either adapt one component, leaving the other mismatched and creating a bottleneck, or jointly select surrogate--acquisition pairs under a shared criterion, overlooking their distinct roles: surrogate selection depends on predictive reliability, whereas acquisition adaptation should respond to campaign context.In this paper, we propose DASH, a Decoupled Adaptive Surrogate--Acquisition Harness for large-language- model (LLM)-enhanced AutoBO. DASH selects surrogates by predictive reliability, uncertainty calibration, and ranking consistency; its two-stage acquisition controller periodically reallocates quotas across acquisition functions, builds a BO shortlist accordingly, and delegates final selection to an LLM. DASH also incorporates an integrated harness, consisting of knowledge-guided warm start and structured memory, to ground optimization in domain knowledge and accumulated feedback. Across four chemical optimization tasks, DASH outperforms the best AutoBO baseline by 12.51% in trajectory-level Acceleration Factor and 5.00% in endpoint Enhancement Factor. Results remain strong across LLM backbones, and ablations verify the complementary contributions of all components. Full-table and behavioral contamination checks find no detectable evidence that direct benchmark memorization or source-cell leakage explains these gains.

In Non-Intrusive Load Monitoring (NILM), adaptive segmentation of electricity consumption time series is critical for appliance recognition. However, prevailing methods face challenges including heuristic parameter tuning, boundary sensitivity, and metric saturation. This paper proposes BayesSeg, a unified framework integrating time-series segmentation, multidimensional evaluation, and automatic parameter optimization. The segmentation layer employs a dual steady-state criterion based on the tail value and mean of preceding subsequences, combined with a sequential extraction and complement-set parsing strategy, to achieve precise unsupervised partitioning of steady-state and transition-state segments. The evaluation layer maps segmentation results to binary state sequences and formulates a composite metric integrating an event-level F1 score (event_F1) with Normalized Mutual Information (NMI). The event_F1 quantifies switching-event precision and recall via tolerance matching, while NMI captures global structural consistency, jointly overcoming the boundary sensitivity and limited discriminability of point-wise metrics. In the optimization layer, the composite score serves as the objective function for Bayesian optimization, which constructs a TPE surrogate model for efficient global parameter-space exploration. Experiments on the SustDataED2 dataset demonstrate that Bayesian optimization requires only ~100 objective evaluations to locate a parameter region within 0.35% deviation of the exhaustive grid-search optimum. The framework achieves a weighted composite score of 0.7149 and an event_F1 of 0.9340 while reducing optimization latency from ~5300 seconds to under 1 second, a speedup exceeding 5700x. BayesSeg automates segmentation configuration and provides a scalable, efficient solution for time-series analysis in NILM and related domains.

Bayesian optimization (BO) has become the standard tool for sample-efficient optimization and owes its efficiency to uncertainty-aware search driven by generic statistical priors. Richer domain priors can improve BO in principle, but encoding them through tailored kernels or problem structure is difficult and rarely done in practice. LLMs can help sidestep this difficulty by making informal priors from natural language, code, and documentation directly available to the optimizer. However, existing LLM-based BO methods either insert the LLM into a fixed role (surrogate, acquisition proxy, or configuration interface) or hand it broad control, sacrificing the systematic exploration that makes BO reliable. We introduce agentic Bayesian optimization: a paradigm in which an LLM agent is the central decision maker in the BO loop while a Bayesian backend provides the uncertainty-aware optimization substrate. The agent configures the problem, queries the backend, selects and commits evaluations, and can revise the optimization strategy during the run by tightening bounds, switching acquisition functions, proposing targeted evaluations, or even reframing the problem following new instructions or observed evidence. We instantiate this idea in Sara, a surrogate-augmented autoresearch agent, and lenz, a modular BoTorch-based backend that the agent can inspect and modify through a structured interface. Across synthetic and real-world benchmarks, Sara preserves the reliability of state-of-the-art BO without prior knowledge, outperforms LLM-based baselines, and uses natural-language priors to improve beyond standard BO. We further demonstrate the practical value of agentic BO in dynamic settings, where Sara reconfigures the full optimization problem on the fly as requirements change, a capability not previously available in standard BO.

Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance. Here we present a systematic, compute-aware study of BO that evaluates surrogate models along two axes: optimization quality and computational frugality. Across eight benchmark functions and nine real-world datasets spanning materials science, mechanics, robotics, chemistry, and machine learning, we benchmark four surrogate models: Gaussian Processes, Random Forests, NGBoost, and Bayesian Adaptive Spline Surfaces. We show that Gaussian Process-based BO consistently incurs the highest time and memory overhead without delivering superior optimization or sample efficiency. In contrast, scalable alternatives achieve equal or better performance at a fraction of the computational cost. Motivated by these findings, we introduce a surrogate-recommendation framework that predicts the most suitable BO surrogate from inexpensive dataset characteristics. Together, these results establish FruBO as a reproducible, compute-aware baseline for Bayesian Optimization and provide practical guidance for surrogate selection under limited computational and experimental budgets.

Wavelength selection is one of the important preprocessing methods in near-infrared spectroscopy to improve prediction accuracy and interpretability of spectral data. We formulate wavelength-region selection for sugar content estimation as a binary black-box optimization problem and propose a method based on Bayesian optimization. The proposed method constructs a sparse quadratic surrogate model and sequentially extracts interested wavelength regions by Thompson sampling. Minimizing an acquisition function is performed as a quadratic unconstrained binary optimization problem by simulated or quantum annealing. Experiments show that the proposed method improves the prediction accuracy of partial least squares regression and yields more consistent wavelength regions than genetic-algorithm-based selection and simulated annealing. Under one-bit local perturbations, the selected wavelength regions show minimal fluctuations in root mean square errors between observed and predicted values of a validation set. This local stability suggests that our method converges to a smoother error landscape and avoids isolated overfitted solutions. These results indicate that combinatorial Bayesian optimization is a useful framework for robust feature selection in spectroscopic prediction tasks.

Reinforcement learning (RL) has shown remarkable success across a wide range of complex tasks. However, RL outcomes can be highly stochastic, and both expected performance and variability often depend on hyperparameter (HP) configurations. We propose efficient and risk-averse heteroscedastic Bayesian Optimization (ERAHBO), a Bayesian optimization method that models both the mean and variance of learning outcomes as functions of the HP configurations. ERAHBO aims to identify HP configurations that achieve high average return while reducing variability across training runs, and it improves the sample efficiency of the HP optimization via adaptive re-sampling rather than a fixed budget per HP. Empirical evaluations across diverse RL algorithms and environments demonstrate that ERAHBO generally outperforms both risk-neutral and risk-averse baselines, delivering improved sample efficiency for risk-averse returns.

Sampling-based methods offer a principled approach to uncertainty quantification in Bayesian neural networks. Their practical use, however, is often challenged by the computational cost of exploring high-dimensional and multimodal posterior distributions. To overcome these difficulties, Bayesian Deep Ensembles, i.e., warmstarting the sampling from several optimized solutions, have proven to be an effective strategy. In this paper, we demonstrate that curvature estimates computed during the warmstart as a byproduct in adaptive optimizers such as AdamW can inform the sampling phase at negligible additional cost. Specifically, our proposed preconditioned sampling strategy based on optimizer-derived geometries can substantially reduce or even eliminate the need for a lengthy sampling burn-in phase and leads to greater numerical stability. This approach consistently maintains or improves predictive performance and uncertainty quantification without any additional computational costs. We confirm the consistency of our findings across various datasets and network architectures.

Autonomous laboratories automate experimental execution, but a campaign must also decide which recovery pathway merits optimization. We formulate this as a sequential decision problem with a discrete pathway-identification stage and a continuous within-pathway optimization stage under heterogeneous experimental costs. Our implementation, Coactive learning, combines a cost-sensitive Bayesian hypothesis-discrimination policy motivated by EC2 (Golovin et al., 2010) with Gaussian-process Bayesian optimization (Srinivas et al., 2010). Under explicitly stated assumptions, the expected spend of one fixed-budget campaign attempt is bounded by the expected pathway-identification cost plus the capped within-pathway optimization budget. We evaluate the method on synthetic benchmarks constrained by selected results reported for PNNL's CICERO selective-precipitation study (Ritchhart et al., 2026). The method performs comparably to an oracle-pathway Bayesian-optimization reference and to a strong split-plate baseline that discriminates pathways with its first plate, without receiving an oracle label for the correct pathway. It is given a candidate hypothesis space and a diagnostic likelihood model. On an NdFeB-inspired instance, it avoids the simulated penalty of a commit-first baseline that initially selects a plausible but inferior hydroxide pathway. This hypothetical wrong-first-commitment scenario is motivated by the hydroxide-oxalate performance contrast reported by CICERO. We characterize the sensitivity of these conclusions to the assumed cost model. The code and benchmark are open source.

Expensive constrained optimization problems in real-world industry design often involve constraint thresholds that are difficult to determine in advance. Engineers may need to adjust constraint thresholds to explore different feasibility-performance trade-offs, requiring solutions under a wide range of threshold settings. However, existing constrained Bayesian optimization methods treat each threshold configuration independently, leading to repeated optimization and failing to exploit the shared relationship among continuously varying thresholds. To address this challenge, we propose constraint-bound agnostic Bayesian optimization (CBA-BO), a learning-based framework that learns a parametric constraint model mapping thresholds to optimal solutions. Once learned, CBA-BO directly predicts solutions for arbitrary unseen threshold configurations without additional optimization, with a one-step Bayesian optimization refinement further improving solution quality. Experiments on benchmark and engineering problems demonstrate that CBA-BO learns a transferable threshold-solution mapping, enabling efficient prediction and optimization for arbitrary threshold queries. An intent-guided constraint-bound recommendation mechanism is further developed to improve objective performance while satisfying user-specified constraint preferences.

Expensive black-box optimization is ubiquitous in science and engineering, where function evaluations are costly and the evaluation budget is limited. Traditional evolutionary algorithms and Meta-BlackBox Optimization (MetaBBO) approaches typically consume most evaluations on candidate selection, often wasting precious budget on inferior solutions. Although surrogate-assisted evolution and Bayesian optimization aim to reduce evaluations through surrogate models, constructing an accurate global model from limited data remains challenging, and model bias can easily trap the search in local optima. To overcome these limitations, we propose NeurGO, a generative MetaBBO framework that directly synthesizes elite candidates from historical population states. Specifically, we employ an attention-based encoder to capture the population-level search trend and condition a decoder on this representation to generate high-quality candidates, avoiding the expensive evaluation of large offspring pools. We then design a quality-diversity loss to maintain solution quality and population diversity throughout the search. Through extensive benchmarking on CEC 2008 and the COCO BBOB test suites, our method achieves better optimization performance under the same evaluation budget and exhibits faster convergence.

Self-driving laboratories increasingly rely on multi-fidelity Bayesian optimization (MFBO) to balance cheap, approximate evaluations against scarce, expensive ones, with a predictive surrogate at its core. Gaussian processes (GPs) are the default choice, but they scale poorly as data accumulate and assume a smooth landscape that molecular and materials search spaces routinely violate. Transfer learning offers an alternative suited to this regime: it learns a representation from abundant cheap data and adapts it to sparse expensive data. Despite its use in property prediction, transfer learning has not been tested as the engine of a closed-loop optimization. Here we benchmark eleven transfer-learning surrogates against four GP methods under an identical selection rule, fidelity budget, and model size, across nine tasks spanning synthetic functions to real chemistry and materials problems. GPs win on smooth, low-dimensional functions but perform worst on molecular and materials problems, where transfer-learning surrogates reach substantially better solutions using far less computation. Because acquisition policy is held fixed across surrogates, this advantage is attributable to the surrogate itself. Uncertainty-driven exploration is not reliably beneficial, and calibration does not predict optimization performance, so greedy exploitation of the transfer-learned mean is the more robust default. Transfer learning is therefore the surrogate of choice for molecular and materials MFBO.

Bayesian optimization (BO) is an optimization method that sequentially proposes the next candidate explainable variables for optimizing target variables by balancing exploration and exploitation. BO is often used under a limited evaluation budget, such as hyperparameter tuning of deep learning. Despite its effectiveness, conventional BO may have poor convergence in practical experimental science where each evaluation is often costly and time-consuming. Recently, BO methods have been proposed that accelerate optimization by using pseudo-experimental data that simulate experimental data. However, when only a limited number of experimental data are available, the generated pseudo-experimental data may be of insufficient quality. In this study, we developed PolyBO to improve optimization time by generating high-quality pseudo-experimental data even when the number of trials is limited. PolyBO performs BO efficiently by generating pseudo-experimental data with an adaptively updated versatile parametric model. This low-capacity polynomial regression model is intended to enable efficient BO even with limited experimental data. PolyBO updates the BO surrogate model with a combined dataset consisting of experimental data and pseudo-experimental data and then performs optimization. Using synthetic benchmark functions with diverse landscapes, we found that PolyBO reduced the optimization time by a median of 42%. For a real-world material composition optimization problem, PolyBO reduced the optimization time by a median of 96% compared with conventional methods. Overall, PolyBO achieves efficient optimization in settings where each experiment requires a long time.

Near 1310 nm photonic-crystal surface-emitting lasers (PCSELs) are attractive narrow-beam sources for optical communication and sensing, but their final design refinement is costly. Small geometry changes simultaneously shift the band-edge resonance, cavity leakage, far-field divergence, and the numerical stability of a high-$Q$ decay fit, while every full-wave trial requires a time-domain simulation. We couple a commercial finite-difference time-domain solver to a reliability-aware Bayesian optimization (BO) loop over eight local design variables. Each completed simulation updates the surrogate used to choose the next geometry. Candidate ranking combines wavelength and beam-quality requirements with a reliability-adjusted metric $Q_{\mathrm{eff}}$ derived from the solver-reported relative fit-error estimate $dQ/Q$. Across three 80-evaluation runs from the same reference model, BO produced 5--15 candidates per run that passed the joint filter. Designs reconstructed from fresh model copies retained $Q_{\mathrm{eff}}=4.33\times10^6$--$7.76\times10^6$, a 60--108-fold increase over the baseline metric, at 1308.23--1310.90~nm with approximately $0.84^{\circ}$ divergence. Under equal budgets, BO gave the highest mean strict-filter yield (9.0 candidates), compared with differential evolution (7.0) and Latin-hypercube sampling (1.5), although the controls occasionally matched the peak $Q_{\mathrm{eff}}$. Field maps, resonance spectra, and local perturbations further identify an index-related wavelength handle and a hole-size-related leakage handle. The resulting FDTD budget produces a pool of wavelength-compatible, narrow-beam, and reproducible high-$Q$ PCSEL candidates without trusting a single optimistic decay fit.

Time-series foundation models can forecast across heterogeneous domains without task-specific training, but their forecasts are fixed once produced and cannot directly incorporate task-specific expert feedback. We study expert-guided forecast editing: a frozen foundation model generates candidate future trajectories, and an expensive expert evaluator scores them to guide forecast revision. Under a tight query budget, two natural strategies sit at opposite ends: best-of-$N$ purely exploits the foundation model's predictive distribution, while optimization approaches mostly explore the forecast horizon as an unstructured high-dimensional vector. Each extreme is individually sub-optimal. We introduce \textbf{DEFT}, an expert-guided forecast editing framework that balances the two by first exploiting the foundation model's predictive samples in a decomposed trend--seasonal space, then exploring around them via component-wise refinement. DEFT queries the expert only on complete trajectories, then reuses scores for the trend and seasonal components that appeared in the queried recombinations. This lets each expert query provide structured component-level feedback while keeping the foundation model frozen. We compare DEFT against direct search approaches, including best-of-$N$, cross-entropy methods, and Bayesian optimization, under matched expert-query budgets. Across two forecasting benchmarks consisting of 78 datasets, three time-series foundation models, four feedback types, and seven query budgets, DEFT consistently improves the effectiveness of expert guidance. A molecular-dynamics case study further suggests that the same principle extends to more physically grounded feedback, supporting the hypothesis that sparse test-time guidance should be spent balancing prior exploitation with structured exploration.

With growing surgeon shortages, automating surgical sub-tasks such as tissue dissection offers a promising step toward reducing workload and expanding patient access. Prior work has relied on hand-crafted incision policies that cannot quantify uncertainty or has relied on simulation-based methods that require strong modeling assumptions. We instead view tissue attachment identification as an inherently probabilistic problem and propose a Bayesian approach that avoids explicit tissue modeling. Our method uses a Sequential Bayesian Hilbert Map (SBHM) to represent the likelihood that each tissue point is attached to the underlying resection surface. An ensemble of learned classifiers predicts attachment likelihoods from spatial data acquired during robotic tissue retraction, with each classifier serving as a noisy information source to update the SBHM. To plan the next retraction, we devise Bayesian Retraction Optimization (BRO) to select the most informative action under safety constraints. As the SBHM refines over time, regions with high attachment likelihood are selectively incised. We validate our method in simulation across diverse tissue geometries and acquisition strategies, and demonstrate zero-shot transfer to real robotic dissection experiments.

Calibration of grey-box simulation models is a constrained optimization problem in which model evaluations are expensive, the parameter space can be high-dimensional, and the search must respect plausibility constraints. Although the simulation code is fully available to the analyst, the joint effect of multiple parameters remains difficult to predict analytically. Classical optimizers such as Nelder--Mead (NM) are simple to deploy but sample-inefficient, particularly under constraints. Modern Bayesian Optimization methods achieve competitive solutions with far fewer evaluations but require non-trivial modeling machinery for constraint handling. We introduce an agentic calibration method in which a large language model acts as the optimizer, with constraints incorporated as a plain-language section of the system prompt. We evaluate the agentic method, NM, and Bayesian Optimization (BO) on an anal cancer simulation model under both unconstrained and clinically constrained calibration. Under unconstrained calibration, the agentic method achieves substantially lower best error than BO and NM, while requiring fewer model evaluations. Under constrained calibration, the agentic method reaches comparable error levels and both outperform NM. These results are obtained at the cost of increased inference time per iteration. Agentic calibration achieves competitive performance with substantially fewer model evaluations, and constraint handling is essentially free at the modeller-facing interface through simple textual specifications rather than additional modelling machinery. The main trade-off lies in increased per-iteration inference cost, making the approach particularly suitable when simulation time dominates. Beyond performance, the per-iteration rationale makes the search auditable and explainable, so its decisions can be scrutinised and justified to third parties.

Collective problem solving often requires that group members consider the tradeoff between exploitation of known solutions and exploration for new ones, where information of known solutions can be disseminated among individual members through communication networks. The Mason--Watts experiment (PNAS 2012) showed that human groups in shorter-path networks outperform those in longer-path networks on a two-dimensional search task. In this work, we focus on the investigation of such network-efficiency effects in the setting of a group of large language model (LLM) agents. Specifically, we consider groups of sixteen LLM agents playing the Mason--Watts experiment on the eight Mason--Watts network topologies. Moreover, we develop mechanistic Bayesian optimization agents such that the performance of LLM agents can be compared with both the mechanistic agents and the human experimental data. Our computational experiments indicate that the LLM agents show a significant network-efficiency effect when instructed to randomize their first-round choices, but not under the default initialization. In this experiment, adding a one-sentence first-round randomization instruction improves collective payoff by more than three times the estimated payoff difference across the eight network topologies. Also, the Bayesian optimization agents obtain higher payoffs than the evaluated LLM agents on this spatial search task. We further compare the agents' exploration--exploitation behavior, copying, and spatial diversity.

Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use. In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.

Molecular optimization in drug discovery, materials design, and catalysis requires searching vast chemical spaces under tight evaluation budgets, since high-fidelity oracles and experimental measurements are costly. The practical impact of an optimization method therefore hinges on its sample efficiency: how few evaluations it needs to find strong candidates. We introduce Sample Efficient Generative Optimization (SEGO), a framework for Bayesian optimization on adaptively generated molecules. In SEGO, a probabilistic surrogate model forms a hypothesis about where hits lie in chemical space, a generative model is steered to propose candidates in that region, the most promising candidate is selected via an acquisition function, and the resulting oracle call is used both to sharpen the surrogate and to anchor the generator in real reward. SEGO attains state-of-the-art performance on the practical molecular optimization (PMO) benchmark using only one tenth of the oracle calls consumed by other methods, and on a multiparameter docking task it reaches ten hits in roughly half the oracle calls of existing approaches. These gains move molecular optimization closer to campaigns driven by direct experimental feedback.

We propose a collaborative meta-learning framework for distributed Bayesian optimization matching centralized performance without raw-data exchange. We show gradient sharing leaks client observations, with leakage worsening as the search converges and queries concentrate near the optimum. We evaluate a differentially private defense and characterize its privacy-utility trade-off.

Bayesian optimization is increasingly used to guide data-efficient experimentation in chemistry, materials science, and related laboratory settings, but its practical performance depends strongly on how well surrogate-model assumptions match the geometry and noise structure of the underlying objective. We introduce tidyHEBO, a robust Bayesian optimization model inspired by heteroskedastic evolutionary Bayesian optimization (HEBO) for single-objective, sequential optimization. tidyHEBO reconstructs the HEBO design philosophy in BoTorch and revises surrogate training, output-warping selection, acquisition function evaluation, and Pareto-front search. We benchmarked tidyHEBO on synthetic functions, Olympus emulators, fully experimental reaction-optimization datasets, needle-in-a-haystack (NIAH) materials problems, and Bayesmark hyperparameter optimization tasks. On these tasks tidyHEBO achieved competitive to superior performance and improvement in robustness across repeated optimization runs. We therefore propose tidyHEBO as a practical tool for sequential experimentations and a strong general-purpose benchmark for future Bayesian optimization research.

Bayesian optimization routinely warm-starts a target experiment with data from related source tasks, and the multi-task Gaussian process is the textbook surrogate for the job. We revisit this default in a controlled setting and find that it misestimates the cross-task correlation even in the simplest non-trivial case, affinely related source and target tasks, where a working transfer learning method should obviously succeed. We trace the failure to two independent structural mechanisms. Per-task standardization, the textbook fix for the affine slice ambiguity, propagates a finite-sample alignment error into the recovered correlation. The marginal likelihood itself identifies the correlation only at a per-sample rate that a Gaussian process at non-overlapping designs further dilutes. We propose three conservative remedies that follow from the analysis: promoting per-task means and scales to model parameters, restricting the task covariance to non-negative correlations, and co-locating part of the source and target designs. Across synthetic multi-task problems and surrogate-based hyperparameter tuning transfer, these remedies recover the target-only baseline on the simple instances, while the broader failure persists on harder instances and across most rank-based and latent-context variants.

This study presents a multi-fidelity framework for the systematic optimization of genetic algorithm (GA) hyperparameters. The framework integrates three fidelity levels: high-fidelity Fast Fourier Transform (FFT) homogenization for validation, a medium-fidelity 3D convolutional neural network surrogate for rapid property evaluation, and a low-fidelity Gaussian process (GP) surrogate within a Bayesian optimization (BO) framework to guide the hyperparameter search. Various acquisition functions are evaluated, with logNEI achieving the best performance by effectively accounting for the noise inherent in GA evaluations. The proposed framework identifies hyperparameter configurations that enable a 25-generation GA run to achieve elastic modulus values comparable to those obtained in a full 75-generation optimization. Furthermore, introducing a penalized BO objective significantly reduces the number of required lattices with only minor decreases in absolute achieved elastic modulus, revealing a practical trade-off between performance and the number of structures that must be evaluated. High-fidelity FFT validation verifies the effectiveness of the surrogate-driven optimization strategy. The optimized hyperparameters allow for rapid convergence, eliminate the need for lattice mutation, and reduce the overall computational cost by 24% (from 225 to 171 hours) while preserving mechanical performance. These results demonstrate the potential of multi-fidelity optimization as an efficient and practical approach for GA hyperparameter tuning and future experimental lattice design studies.

In many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizes an objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.

Designing effective multi-objective Bayesian optimization (MOBO) algorithms requires balancing many interdependent design choices whose optimal configuration is problem-dependent and typically demands deep expertise. We extend the LLaMEA framework to MOBO, using large language models as mutation and crossover operators within evolutionary strategies to generate complete algorithm implementations, with SMAC hyperparameter optimization integrated into the evolutionary loop. Across nine evolutionary runs we generated approximately 900 algorithms and benchmarked them on twelve synthetic problems (ZDT, DTLZ, WFG) and three real-world engineering problems (RE), using a BoFire qParEGO implementation as a state-of-the-art Bayesian-optimization baseline. On the synthetic suite the strongest generated algorithm attains the highest mean normalized hypervolume (0.971, vs. 0.869 for qParEGO) while requiring roughly 60x less wall-clock time; a Friedman test with post-hoc analysis places the two in a single top-performing group, and per-problem tests find the generated algorithm significantly better than qParEGO on 7 of the 12 problems and never worse, matching state-of-the-art accuracy at an order-of-magnitude lower cost. On the three unseen real-world engineering problems a generated algorithm attains the best mean normalized hypervolume (0.985, vs. 0.971 for qParEGO)--significantly better than qParEGO on two of the three problems--at roughly 3.4x lower wall-clock cost, confirming that the gains transfer beyond the synthetic regime. LLM-driven evolutionary search can thus discover algorithm designs that achieve Pareto-efficient trade-offs difficult to reach through manual design.

Bayesian Optimization (BO) generally begins with an initialization phase: a batch of $n_0$ uninformed evaluations. The choice of $n_0$ remains largely heuristic, and we empirically observe that the total cost (random initial points plus BO iterations needed to find the global optimum) is U-shaped in $n_0$, i.e., a practitioner wastes resources by selecting either too low or too high a value of $n_0$. We find this tradeoff persists across MLE, Bayesian MCMC, and exact GP hyperparameters, as well as across acquisition functions. Toward the latter, Thompson Sampling appears an exception, with both total cost and simple regret essentially $n_0$-agnostic, though higher in our experiments. We attribute this U-shape to the known boundary issue of variance-driven BO: BO burns early budget on corners of the hypercube before turning inward. We demonstrate this effect using a 3D BO trajectory where the exact hyperparameters are known. We conclude with practical recommendations: use multi-step lookahead BO where possible; otherwise use Thompson Sampling when $n_0$ cannot be tuned, and a generously large $n_0$ when it can.

Industrial automation increasingly demands control strategies that balance operational performance with strict energy efficiency requirements. A common approach to solving this multi-objective problem, particularly within the framework of reinforcement learning (RL), is to formulate a single, scalar reward function that linearly combines the competing objectives. However, the manual weighting of these different objectives is heavily reliant on domain intuition, incredibly time-consuming, prone to human bias, and frequently fails to uncover optimal trade-off solutions. This work addresses the critical challenge of automating the weight selection process to systematically and efficiently discover the Pareto front of optimal trade-off policies. We formulate the weight selection process as a multi-objective Bayesian optimization (MOBO) problem and evaluate its sample efficiency against a standard uniform grid search baseline. Using a physical Quanser Aero 2 testbed configured for 1-DoF pitch control, our results demonstrate that the MOBO approach, utilizing the expected hypervolume improvement (qEHVI) acquisition function, consistently outperforms uniform grid sampling. MOBO achieves superior hypervolume and maximum spread, successfully identifying high-quality, diverse trade-off policies with a reduced evaluation budget, thereby enabling highly efficient energy-aware control in complex mechatronic systems.

In many scientific and engineering domains, maximizing discovery within a limited sampling budget demands strategic, observation-guided exploration. While generative models have enabled training-free reward alignment, current methods typically excel in local searches within narrow regions of the underlying distribution. These approaches struggle when preferences are unknown a priori and only revealed through sequential feedback-a scenario demanding broad exploration to uncover high-utility regions. To address this, we introduce Bootstrap Flow-Map-Tree (a.k.a BFMT), a novel computationally efficient sampling framework designed for history-aware global search and alignment under sampling budget constraints. BFMT enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling. By enabling dynamic transition time steps scheduling, BFMT efficiently allocates its sampling budget, smoothly transitioning from broad global exploration to fine-grained local refinement of high-utility modes discovered through exploration. Extensive experiments and ablations across diverse search and alignment tasks demonstrate that BFMT substantially outperforms baseline approaches.

Bayesian Optimisation (BO) under unknown constraints is particularly challenging when feasible regions are small. In such settings, existing methods that typically rely solely on evaluations of the true objective and constraints struggle to efficiently explore the design space. However, many real-world applications offer auxiliary data sources (e.g. surrogate models or simplified simulations) that can support early exploration. Despite this potential, their integration into constrained BO remains largely unexplored. We propose a general multi-source framework that extends constrained Max-value Entropy Search, capturing inter-source correlation while balancing evaluation cost and information gain. Experiments on both synthetic and physics-based benchmarks show that our method efficiently identifies feasible and optimal solutions, even when auxiliary data are only weakly correlated. The proposed approach consistently outperforms existing methods, particularly in early-stage exploration.

Modern engineering workflows increasingly rely on massive parallel simulation, driving the need for scalable, large-batch Bayesian Optimization (BO). Existing batch BO methods, however, incur large computational cost or rely on approximations that erode batch diversity. We propose B3O (Boltzmann Batch Bayesian Optimization), a framework that reframes batch generation as a pure sampling problem: drawing samples directly from the Boltzmann distribution defined by the acquisition function avoids the bottlenecks of existing large-batch methods. Theoretically, we prove that queries sampled from this distribution incur only negligible additional regret. Empirically, B3O outperforms existing batch BO methods on standard synthetic benchmarks and adapts robustly across complex applied tasks, including multi-objective electrode design and mixed-variable race car configuration.

This paper presents BOWConnect, a bidirectional parallel kinodynamic motion planner that addresses three fundamental limitations of existing sampling-based methods: sample inefficiency in high-dimensional state spaces, unreliable cost heuristics under dynamic constraints, and poor performance in narrow passage environments. Unlike classical planners that rely on random control sampling and geometric distance heuristics, BOWConnect integrates Bayesian Optimization over Windows (BOW) as a learning-based steering function within a parallel tree-based exploration framework, enabling each worker to learn local cost maps and constraints to guide sampling toward dynamically feasible and collision-free controls. A bidirectional architecture simultaneously grows forward and backward trees from the start and goal regions in parallel threads, with a spatial hashing mechanism enabling fast connection queries and a boundary value problem solver generating kinodynamically consistent bridge trajectories. Extensive evaluations across ten benchmark environments demonstrate that BOWConnect achieves 100% success while delivering the fastest or near-fastest planning time in complex scenarios, including narrow passages and non-convex spaces where state-of-the-art planners fail or degrade substantially. Real-world deployment on a ground vehicle and a quadrotor confirms real-time planning with no collisions. Videos of real-world and simulated experiments, high-resolution versions of the figures, and the open-source code are available at https://bow-connect.github.io/.

Identifying high-utility candidates from massive discrete spaces under expensive evaluations is a recurring challenge across the sciences, with structure-based drug discovery as a prominent example. While surrogate-based optimization can increase sample efficiency by reducing the number of expensive evaluations, modern molecular libraries have reached billions to trillions of compounds, making full-library surrogate inference itself a major computational bottleneck. We introduce BOBa, a bandit-guided surrogate optimization framework that eliminates full-library inference by adaptively allocating computation across partitions of the action space. By treating partitions as arms in a multi-armed bandit, BOBa concentrates inference and evaluations on empirically promising partitions while maintaining principled exploration. Experiments on real-world synthesis-on-demand libraries demonstrate that optimism-under-uncertainty bandits, combined with meaningful action space partitioning, are essential for effective allocation of inference and evaluations. Our findings reveal a tunable tradeoff between screening performance and surrogate inference cost, which supports practical optimization over current libraries, and establishes a viable route to ultra-large library virtual screening.

Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.

Efficient sorter diversion control of automated material handling systems (MHS) is critical for optimizing operational efficiency in large-scale warehouse environments. In this study, we use an inbound receiving sorter at a high-volume e-commerce warehouse as our primary use case, where the sorter diversion system relies on cost functions with static weight configurations that fail to adapt to highly dynamic system contexts, such as volume mode, congestion level, equipment physical status, and upstream/downstream dependencies. To address this real-time sorter diversion optimization challenge, we conducted a comparative study of three candidate hybrid machine learning frameworks: Linear Regression with Gradient Descent Optimization (LR+GDO), XGBoost with Bayesian Optimization (XGB+BO), and Bayesian Contextual Bandits (BCB). Model training and evaluation were enabled by leveraging a high-fidelity physics-aware emulator to overcome the cold-start problem and allow a safe transition from offline to online learning. We performed comprehensive evaluations including reward model predictive accuracy, contextual sensitivity, action distribution, and projected reward uplift. Our results demonstrate that while tree-based reward models offer slightly better predictive power, the BCB framework achieved overall higher performance with 2.03% reward uplift over the heuristic baseline. Furthermore, BCB exhibits several superior characteristics, such as its decisive time-optimal policy backed by Bang-Bang control theory, continuous online learning capability, strategic balance between exploration and exploitation, and significantly shorter inference latency. These results demonstrate the potential of the BCB framework for real-time control optimization in large-scale warehouse environments, motivating further investigation toward operational deployment.

Configuring the hyperparameters of Mixed-integer programming (MIP) solvers is a high-dimensional, instance-dependent optimization problem where suboptimal settings can degrade solving time by orders of magnitude. Default configurations are often suboptimal, while traditional tuning methods either suffer from the ``cold-start'' problem and inefficient search or heavily rely on expert experience. This paper introduces \textbf{GRIMIP} (\textbf{\underline{G}}eneral \textbf{\underline{R}}easoning for \textbf{\underline{I}}nstance-specific \textbf{\underline{MIP}} configuration), a novel hybrid intelligence framework that synergistically integrates the semantic reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). GRIMIP enables the LLM to function as a complete probabilistic surrogate within the BO loop, significantly improving performance and reducing sampling and evaluation costs. On seven benchmarks including MIPLIB, GRIMIP achieves over 40% reduction in Primal-Dual Integral on hard instances, outperforming SMAC and other LLM-assisted BO methods. By granting LLMs sufficient autonomy, GRIMIP combines the expert-level reasoning of LLMs with the efficient search of BO, achieving state-of-the-art performance.

Machine-learned interatomic potentials now enable efficient atomistic evaluation for interactive materials discovery, yet closed-loop crystal search methods remain fragmented across bespoke pipelines for editing, relaxation, scoring, constraints, and bookkeeping. We introduce SciVerseGym, a Gymnasium-compatible environment for sequential crystal discovery that frames crystal design as a Markov decision process. Agents observe an atomistic structure, apply chemically meaningful edits, and receive feedback from a configurable evaluator. SciVerseGym supports local and global actions, including elemental substitution, lattice perturbation, atomic displacement, vacancy creation, and atom insertion, along with configurable chemical spaces, structure pools, atomistic and graph-based observations, custom rewards, optional relaxation, and stability or phonon-related diagnostics. Each step applies an edit, evaluates the candidate using a machine-learned interatomic potential or any ASE-compatible calculator, and returns the standard (obs, reward, terminated, truncated, info) tuple. By decoupling agent logic from materials infrastructure, SciVerseGym provides an open, reproducible, and extensible testbed for reinforcement learning, Bayesian optimization, evolutionary search, and language-agent workflows in closed-loop crystal discovery. Code is available at: https://github.com/Bin-Cao/SciVerseGym.

We introduce BASIL, a user-friendly desktop application for process optimization. BASIL employs a Bayesian approach, incorporating special acquisition functions that can be used to solve both single and multi-objective optimization problems. It provides a graphical interface that enables users to input their experimental parameters, optimization objectives, and legacy data. This is then used to build surrogate models, which are coupled with acquisition functions to guide and optimize a process towards a desired objective. To facilitate model building, BASIL provides a variety of predefined surrogate model templates. BASIL can be used to optimize any arbitrary experiment or process with known, user-defined input variables, optimization objectives, and defined output.

This work presents an extension to Pareto Front Guided Sampling (PFGS), a Human-in-the-Loop (HitL) Bayesian Optimization (BO) framework in which Gaussian process (GP) surrogate-derived quantities are reformulated as objectives of a multi-objective optimization problem, and the resulting Pareto front is exposed to a domain expert for interactive candidate selection rather than returning a single automated recommendation. The framework is extended in two directions: constrained optimization is addressed by incorporating the posterior probability of satisfying output specification limits as an explicit Pareto objective, computed analytically from the GP posterior distribution; robust optimization is addressed by a Monte Carlo sampling strategy that estimates expected lower-confidence performance over a user-defined variability of input perturbations, capturing performance degradation under likely implementation deviations. The resulting multi-dimensional Pareto representation renders trade-offs between predicted performance, model uncertainty, probabilistic constraint satisfaction, and input robustness simultaneously visible through pairwise two-dimensional projections on an interactive dashboard, enabling selection criteria to be iteratively refined as the surrogate model improves and development objectives evolve. The framework is showcased on an eight-dimensional fed-batch Chinese Hamster Ovary (CHO) cell culture simulator demonstrating systematic identification of high-performing, feasibility-compliant, and perturbation-resilient operating conditions, and illustrating how expert-defined requirements provide a principled stopping criterion and support informed allocation of experimental resources.

In many materials and product design problems, desirable candidates exhibit properties that fall within an acceptable range rather than achieve a single optimum. Recovering multiple, distinct solutions that satisfy such specifications is also practically valuable, as some candidates may be preferred for reasons of cost, processability, or robustness that are difficult to encode directly in an objective function. Here, we develop a range-aware Bayesian optimization (BO) framework in which the acquisition function directly scores the posterior probability that a candidate satisfies a target range. The framework naturally extends to parallel pursuit of multiple distinct specifications over a shared candidate space. Across benchmark tasks, range-aware acquisition consistently recovers larger and more diverse sets of valid designs than standard BO baselines and recent goal-seeking methods. Its utility is further demonstrated in two practically motivated design case studies involving optimizing reaction conditions for polymer synthesis and sequence-defined oligomer discovery for prescribed optical absorption bands, supported by quantum chemical calculations. These results suggest that range-aware BO can provide a practical and sample-efficient foundation for specification-driven design, particularly when design flexibility and solution diversity are important considerations.

Real-time autonomous navigation in dynamic, unknown environments remains a fundamental challenge for mobile robotics. We propose a map-free framework that tightly integrates reactive rolling-horizon planning with nonlinear Model Predictive Control (MPC). At each control cycle, a LiDAR-based Gaussian occupancy representation is constructed and used to generate collision-free trajectories via A* search, which are then tracked by a CasADi/IPOPT MPC formulation incorporating a smooth sigmoid obstacle barrier. To improve robustness to parameter sensitivity, we adopt an offline Bayesian optimization scheme based on Tree-structured Parzen Estimators (TPE), which identifies near-optimal controller parameters with respect to a composite navigation objective. In addition, a Gaussian Process surrogate is used to analyze parameter sensitivity and provide insight into the optimization landscape. The proposed framework is robot-agnostic and is evaluated on the Unitree Go2 quadruped in simulation using Gazebo, followed by deployment on the physical robot. Experimental results show that parameters tuned in simulation transfer effectively to hardware, maintaining comparable performance without additional tuning. The full system achieves up to a 90.0% navigation success rate when deployed, along with a 38.9% average improvement in the evaluation metrics across simulated environments.