Bayesian Optimization

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Overview

Bayesian optimization studies how to find good inputs to an expensive or unknown process—such as a simulation, experiment, or model configuration—using as few evaluations as possible. It typically fits a probabilistic surrogate, often a Gaussian process, then uses an acquisition function to balance trying promising inputs with exploring uncertain ones. Current approaches extend this loop with trust regions, multi-fidelity data, constraints, multiple objectives, changing conditions, and human or language-model guidance. A central challenge is choosing models and search strategies that remain reliable in high-dimensional or structured spaces without making inference and candidate selection too costly; theoretical guarantees do not always predict practical performance.

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243 papers45 papers in the last four weeks, up 36% on the four weeks before. 0.3% of all new papers.

May 19, 2026

Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization

Gaussian process (GP) predictive distributions are commonly used in Bayesian optimization (BO) to guide the selection of evaluation points for expensive objective functions. The choice of kernel and hyperparameters has a strong influence on the exploration--exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on both the probability mass below the current best value and the shape of the predictive distribution in this region. This article studies goal-oriented calibration of GP predictive distributions below a low threshold tt in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. We consider two complementary forms of calibration below tt for inputs distributed according to a reference measure μμ: occurrence calibration over the design space and thresholded μμ-calibration on sublevel sets of the form {x∈X,f(x)≤t}\{x\in\mathbb{X}, f(x)\le t\}. We propose tcGP, a post-hoc method that combines these two forms of calibration for GP predictive distributions below tt. With fixed GP hyperparameters, the exact EI sampling criterion based on tcGP generates a sequence of evaluation points that is dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models.

Aurélien Pion, Emmanuel Vazquez

Transvalor S.A., Biot, France · Univ. Paris-Saclay, CNRS, CentraleSup´elec, L2S, Gif-sur-Yvette, France

Post-Hoc CalibrationBayesian OptimizationGaussian ProcessesUncertainty Calibration
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May 18, 2026

Embedding by Elicitation: Dynamic Representations for Bayesian Optimization of System Prompts

System prompts are a central control mechanism in modern AI systems, shaping behavior across conversations, tasks, and user populations. Yet they are difficult to tune when feedback is available only as aggregate metrics rather than per-example labels, failures, or critiques. We study this aggregate feedback setting as sample-constrained black-box optimization over discrete, variable-length text. We introduce ReElicit, a Bayesian optimization framework based on embedding by elicitation. Given a task description, previously evaluated prompts, and scalar scores, an LLM elicits a compact, interpretable feature space and maps prompts into it. Leveraging a probabilistic Gaussian process surrogate, an acquisition function then selects target feature vectors, which the LLM realizes and refines into deployable system prompts. Re-eliciting the feature space as new evaluations arrive lets the representation adapt to the observed prompt-score history. We evaluate the setting using offline benchmark accuracy as a controlled aggregate proxy: the optimizer observes one scalar score per prompt and no per-example labels, errors, or critiques. Across ten system prompt optimization tasks with a 30 total evaluation budget, ReElicit achieves the strongest aggregate performance profile among representative aggregate-only prompt-optimization baselines. These results suggest that LLMs can serve as adaptive semantic representation builders, not only prompt generators, for Bayesian optimization over natural-language artifacts.

Zhiyuan Jerry Lin, Benjamin Letham, Samuel Dooley +2

Meta

Bayesian OptimizationLarge Language Model-Guided OptimizationAutomatic Prompt OptimizationPrompt Optimization
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May 18, 2026

Automated Kernel Discovery Towards Understanding High-dimensional Bayesian Optimization

Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions for two bottlenecks: their kernel search space is limited to additions and multiplications of base kernels, and LLM-based approaches require conditioning on raw observations, which becomes infeasible due to context-length limits and the difficulty of extracting meaningful patterns. We introduce Kernel Discovery, a LLM-driven evolutionary framework for high-dimensional BO that searches a broader kernel space beyond predefined composition rules and does not require conditioning on observations. Motivated by the observation that directly prompting an LLM to generate kernel code yields syntactically varied but functionally identical kernels, we adopt a two-stage approach: an LLM first proposes novel mathematical forms, then a second LLM call converts each form into validated, executable code. We also propose a leave-one-out continuous ranked probability score (LOO-CRPS) as a selection criterion that penalizes overfitted kernels. On five high-dimensional BO benchmarks, our method achieves an average rank of 1.2 out of 17, outperforming competitive baselines. We further analyze the discovered kernels to identify which kernels lead to improvements in high-dimensional BO.

Taeyoung Yun, Woocheol Shin, Inhyuck Song +2

1Korea Advanced Institute of Science and Technology (KAIST)

Bayesian OptimizationLarge Language Model-Guided OptimizationKernel MethodsGaussian Process Regression
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May 18, 2026

Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery

Scientific discovery is increasingly constrained by costly experiments and limited resources, underscoring the need for efficient optimization in AI for science. Bayesian Optimization (BO), though widely adopted for balancing exploration and exploitation, often exhibits slow cold-start performance and poor scalability in high-dimensional settings, limiting its applicability in real-world scientific problems. To overcome these challenges, we propose LLM-Guided Bayesian Optimization (LGBO), the first LLM preference-guided BO framework that continuously integrates the semantic reasoning of large language models (LLMs) into the optimization loop. Unlike prior works that use LLMs only for warm-start initialization or candidate generation, LGBO introduces a region-lifted preference mechanism that embeds LLM-driven preferences into every iteration, shifting the surrogate mean in a stable and controllable way. Theoretically, we prove that LGBO does not perform significantly worse than standard BO in the worst case, while achieving significantly faster convergence when preferences align with the objective. Empirically, LGBO consistently outperforms existing methods across diverse dry benchmarks in physics, chemistry, biology, and materials science. Most notably, in a new wet-lab optimization of Fe-Cr battery electrolytes, LGBO attains 90% of the best observed value within 6 iterations, whereas standard BO and existing LLM-augmented baselines require more than 10. Together, these results suggest that LGBO offers a promising direction for integrating LLMs into scientific optimization workflows.

Xinzhe Yuan, Zhuo Chen, Jianshu Zhang +4

Shanghai Artificial Intelligence Laboratory, Shanghai, China · Shanghai Jiao Tong University, Shanghai, China · Harbin Institute of Technology, Harbin, China

Bayesian OptimizationLarge Language Model-Guided OptimizationSafe Bayesian OptimizationLarge Language Model-Guided Scientific Discovery
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May 16, 2026

BoLT: A Benchmark to Democratize Black-box Optimization Research for Expensive LLM Tasks

Optimization of LLM training and inference configurations, such as hyperparameters, data mixtures, and prompts, is critical to performance, but it is often approached heuristically in practice, leading to potentially suboptimal outcomes. By framing them as noisy, expensive, and derivative-free optimization problems, Bayesian optimization (BO) and other black-box optimization (BBO) methods offer a promising yet underexplored direction for principled, sample-efficient methods. However, LLM training and inference costs are prohibitively high for most of the BBO research community, and new methods are often only evaluated on synthetic test functions and small-scale datasets that fail to capture the challenges of modern LLM optimization problems. This impedes the development of BBO methods and makes it difficult to assess their effectiveness on modern LLM tasks. We introduce BoLT, the first LLM-centric benchmark that democratizes LLM research for the BBO community. BoLT is released at https://github.com/chewwt/bolt. BoLT covers broad and well-motivated LLM optimization problems, involving multi-fidelity, multi-objective, heteroscedastic noise, and high-dimensional search spaces. Each problem in BoLT is grounded in real experimental data and made fully reproducible and accessible through lightweight surrogate models fitted to the results of thousands of real LLM experiments. We benchmark BoLT against an extensive range of BO and BBO methods, showing that selected BO methods consistently outperform others across tasks and highlighting gaps in existing BBO methods on LLM tasks, underscoring the need to modernize benchmarks for the BBO community.

Ruth Wan Theng Chew, Zhiliang Chen, Apivich Hemachandra +1

National University of Singapore

Bayesian OptimizationBenchmark DesignBlack-Box OptimizationHyperparameter Optimization
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May 13, 2026

Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization

This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.

Jannis Lübsen, Annika Eichler

Institute of Control Systems, Hamburg University of Technology, Hamburg, Germany · Institute of Control Systems, Hamburg University of Technology · Deutsches Elektronen-Synchrotron, Hamburg, Germany

Bayesian OptimizationGaussian ProcessesSafe Bayesian OptimizationMulti-Output Gaussian Processes
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May 13, 2026

Kernel-based guarantees for nonlinear parametric models in Bayesian optimization

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on Gaussian processes, kernel machines, linear models, or linearized neural approximations, leaving a gap between theory and the nonlinear models used in practice. We develop a kernel based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data. Our approach uses kernels over the parameter space to induce reproducing kernel Hilbert space structures over the corresponding model class, yielding confidence bounds for models trained with broad classes of regularized convex losses. We show how these bounds can support convergence guarantees for nonlinear acquisition and surrogate models, including randomized regularized policies that select points by maximizing a trained random model. These results provide a unified route to analyzing nonlinear parametric models in Bayesian optimization and related adaptive optimization settings.

Rafael Oliveira

The Commonwealth Scientific and Industrial Research Organisation (CSIRO) Sydney, Australia

Bayesian OptimizationAdaptive SamplingKernel MethodsStatistical Learning Theory
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May 12, 2026

Efficient Conditioning Why Pseudo Observation Batch Bayesian Optimization Works When It Does not

Constant Liar (CL), Kriging Believer (KB), and fantasy models are widely used for batch selection in parallel Bayesian Optimization, yet a unified theory explaining their effectiveness and conditions under which they fail has been lacking. We identify efficient conditioning as the key surrogate property the ability to update predictions in closed form when data is augmented. We prove that Gaussian Processes satisfy this requirement, producing provably distinct batch points with separation of order l, and that this holds for any acquisition function monotonically non decreasing in posterior uncertainty (EI, UCB, PI), with qualitatively similar behavior for Thompson Sampling. We unify CL, KB, and fantasy models as instances of a single conditioning mechanism differing only in the lie value distribution, and draw quantitative connections to Local Penalization (LP) and qualitative connections to Determinantal Point Processes (DPPs). To disentangle model structure from optimizer randomness, we introduce the Structural Diversity Diagnostic (SDD), a reusable methodology for testing surrogate compatibility. Experiments on Hartmann6D, Ackley 8D, Levy10D, and SVM hyperparameter tuning validate all theoretical predictions: CL or KBs implicit penalty matches or outperforms explicit LP greedy conditioning achieves convergence on par with joint qEI efficient conditioning extends to Multiquadric RBF networks; and parametric surrogates produce degenerate batches even when fully retrained (random forests), while neural networks regain diversity only at 15x the wall clock cost of GP conditioning. Robustness is confirmed across multiple initial datasets and under observation noise.

Kumbha Nagaswetha, Rabi Pathak

Surrogate ModelingBayesian OptimizationGaussian Processes
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May 12, 2026

Elicitation-Augmented Bayesian Optimization

Human-in-the-loop Bayesian optimization (HITL BO) methods utilize human expertise to improve the sample-efficiency of BO. Most HITL BO methods assume that a domain expert can quantify their knowledge, for instance by pinpointing query locations or specifying their prior beliefs about the location of the maximum as a probability distribution. However, since human expertise is often tacit and cannot be explicitly quantified, we consider a setting where domain knowledge of an expert is elicited via pairwise comparisons of designs. We interpret the expert's pairwise judgements as noisy evidence about the values of the observable objective function and develop a principled method for combining the information obtained via direct observations and pairwise queries. Specifically, we derive a cost-aware value-of-information acquisition function that balances direct observations against pairwise queries. The proposed method approaches the convex hull of the trajectories of the individual information sources: when pairwise queries are cheap it substantially improves sample-efficiency over observation-only BO, and when pairwise queries are costly or noisy, it recovers the performance of standard BO by relying on direct observations alone.

Alvar Haltia, Ville Hyvönen, Samuel Kaski

Aalto University · University of Helsinki · Aalto University, University of Manchester

Bayesian OptimizationHuman-in-the-Loop EvaluationBayesian Experimental Design
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May 11, 2026

Online Sharp-Calibrated Bayesian Optimization

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions, commonly based on Gaussian process (GP) surrogate models. Its effectiveness relies on uncertainty quantification that is both sharp (informative) and well-calibrated along the BO trajectory. In practice, GP kernel hyperparameters are unknown and are refit online from sequentially collected (non-i.i.d.) data, which can yield miscalibrated or overly conservative uncertainty and lies outside the fixed-kernel assumptions of standard BO regret theory. We propose Online Sharp-Calibrated Bayesian Optimization (OSCBO), a BO algorithm that adaptively balances GP sharpness and calibration by casting hyperparameter selection as a constrained online-learning problem. We also show that OSCBO preserves sublinear regret bounds by leveraging the theoretical guarantees of the underlying online learning algorithm. Empirically, OSCBO performs competitively across synthetic and real-world benchmarks, ranking among the strongest methods in final simple regret while maintaining robust cumulative-regret behavior.

Marshal Arijona Sinaga, Julien Martinelli, Teemu Turpeinen +1

ELLIS Institute Finland · Aalto University · University of Manchester

Bayesian OptimizationUncertainty CalibrationGaussian Process Regression
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May 11, 2026

Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

Masaki Adachi, Anita Yang, Yakun Wang +1

Toyota Motor Corporation · Lattice Lab · University of Bristol

Bayesian OptimizationBlack-Box OptimizationDiffusion Guidance
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May 11, 2026

Many Needles in a Haystack: Active Hit Discovery for Perturbation Experiments

High-throughput gene perturbation experiments can test several genetic interventions in parallel, yet experimental budgets remain limited. A central goal is hit discovery: identifying as many perturbations as possible whose phenotypic effect exceeds a predefined threshold. Pure exploration strategies are statistically inefficient, wasting budget on low-value regions. Bayesian optimization methods offer a principled alternative but target a single global optimum, over-exploiting dominant modes while neglecting other high-value regions. We formalize hit discovery as a sequential experimental design problem and propose Probability-of-Hit, an acquisition function that directly targets threshold exceedance by ranking candidates according to their posterior probability of being a hit. We prove asymptotic optimality of this approach and demonstrate strong empirical performance on both synthetic benchmarks and real biological immunology datasets, including up to 6.4% improvement over baselines on the Schmidt IL-2 dataset.

Andrea Rubbi, Arpit Merchant, Samuel Ogden +4

Department of Computer Science and Technology, University of Cambridge, Cambridge, UK · Cambridge Center for AI in Medicine, University of Cambridge, Cambridge, UK · MediaTek Research, Cambridge, UK +1

Bayesian OptimizationBayesian Experimental Design
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May 10, 2026

Bayesian Optimization with Structured Measurements: A Vector-Valued RKHS Framework

Bayesian optimization (BO) is an efficient framework for optimizing expensive black-box functions. However, it is typically formulated as learning an end-to-end mapping from inputs to scalar objectives, thereby discarding the potentially rich information whenever a structured system output is available. In this work, we study Bayesian optimization over a vector-valued operator with structured measurements, where each measurement observes multidimensional or functional outputs, e.g., trajectories or spatial fields, rather than a single scalar value. The objective is then defined as a linear functional of these measurements. This allows each observation to reveal substantially richer information about the underlying system compared to scalar observations. Assuming the unknown operator lies in a vector-valued reproducing kernel Hilbert space (RKHS), we derive high-probability concentration bounds for the kernel ridge regression (KRR) estimator directly in the measurement space, characterizing uncertainty in a general Hilbert space. Building on these results, we propose an algorithm based on the upper confidence bound (UCB) acquisition function with regret guarantees under mild assumptions, recovering sublinear rates for common kernels. Empirically, we demonstrate that leveraging structured measurements leads to improved sample efficiency by enabling efficient transfer of information across objectives and adaptation to time-varying settings.

Wenbin Wang, Colin N. Jones

Automatic Control Laboratory, EPFL

Kernel Ridge RegressionBayesian OptimizationKernel Methods
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May 8, 2026

ADKO: Agentic Decentralized Knowledge Optimization

We present Agentic Decentralized Knowledge Optimization (ADKO), a framework for collaborative black-box optimization across autonomous agents that achieves sample efficiency, privacy preservation, heterogeneous-objective handling, and communication efficiency. Each agent maintains a private Gaussian Process (GP) surrogate trained on local data and communicates only through knowledge tokens-compact, lossy summaries containing directional signals, advantage scores, and optional language-model (LM) insights-without sharing raw data or model parameters. ADKO unifies GP-Upper Confidence Bound (GP-UCB), parallel Bayesian optimization, decentralized learning, and LM-guided discovery. We provide the first formal analysis of dual information loss: token compression, quantified via mutual-information-based fidelity, and LM approximation error, decomposed into bias and stochastic noise. Our main result shows cumulative regret decomposes into GP error, LM bias, LM noise, and compression loss, with necessary and sufficient conditions for sublinear regret. We also propose fidelity-aware token pruning to preserve high-information tokens under memory budget. Experiments on neural architecture search and scientific discovery validate the theory and show consistent improvements over strong baselines.

Lucas Nerone Rillo, Zhanhong Jiang, Nastaran Saadati +4

Iowa State University · New York University

Multi-Agent System OptimizationAI Agents for Scientific DiscoveryBayesian OptimizationBlack-Box OptimizationLarge Language Model-Guided OptimizationDecentralized Optimization
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May 8, 2026

Open-Ended Task Discovery via Bayesian Optimization

When applying Bayesian optimization (BO) to scientific workflow, a major yet often overlooked source of uncertainty is the task itself -- namely, what to optimize and how to evaluate it -- which can evolve as evidence accumulates. We introduce Generate-Select-Refine (GSR), a open-ended BO framework that alternates between task generation and task optimization. Starting from a user-provided seed task, GSR generates new tasks in a coarse-to-fine manner while a task-acquisition function schedules optimization. Asymptotically, it concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO. We apply GSR to new product development, chemical synthesis scaling, algorithm analysis, and patent repurposing, where it outperforms existing LLM-based optimizers.

Masaki Adachi, Yuta Suzuki, Juliusz Ziomek

Lattice Lab · Toyota Motor Corporation · Machine Learning Research Group +1

Bayesian Optimization
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May 8, 2026

Ensemble Distributionally Robust Bayesian Optimisation with Continuous Context

We study Bayesian Optimisation (BO) in settings where the objective function is influenced by uncontrollable environmental contexts governed by an unknown probability distribution. In practice, the contextual distribution must be estimated from empirical data, a process that inherently introduces distributional mismatch, producing sub-optimal results. While Distributionally Robust Optimisation (DRO) provides a framework to mitigate these risks, existing robust BO methods frequently suffer from high computational complexity, rely on discretisation of continuous context spaces, or impose restrictive assumptions on the structure of the ambiguity set. To overcome these limitations, we propose Ensemble Distributionally Robust Bayesian Optimisation (EDRBO). Our framework leverages the expressive power of ensemble surrogate models to approximate the black-box function while simultaneously accounting for contextual uncertainty. By utilising Wasserstein ball as ambiguity sets, EDRBO provides a robustified acquisition function that remains computationally tractable and natively handles continuous context spaces. We establish a rigorous theoretical foundation for our approach by proving sublinear cumulative regret guarantees of order O(γTT)\mathcal{O}(γ_T \sqrt{T}), where γTγ_T represents the maximum information gain within the ensemble. Finally, we provide extensive empirical evaluations that corroborate our theory and demonstrate the state-of-the-art performance of EDRBO.

Tigran Ramazyan, Denis Derkach

Faculty of Computer Science, HSE University, Pokrovsky Boulevard 11, Moscow, 109028, Moscow, Russia.

Bayesian OptimizationDistributionally Robust OptimizationWasserstein Distributionally Robust Optimization
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May 7, 2026

ORTHOBO: Orthogonal Bayesian Hyperparameter Optimization

Bayesian optimization is widely used for hyperparameter optimization when model evaluations are expensive; however, noisy acquisition estimates can lead to unstable decisions. We identify acquisition estimation noise as a failure mode that was previously overlooked: even when the surrogate model and acquisition target are correctly specified, finite-sample Monte Carlo error can perturb acquisition values. This can, in turn, flip candidate rankings and lead to suboptimal BO decisions. As a remedy, we aim at variance reduction and propose an orthogonal acquisition estimator that subtracts an optimally weighted score-function control variate, which yields an acquisition residual orthogonal to posterior score directions and which thus reduces Monte Carlo variance. We further introduce OrthoBO: a Bayesian optimization framework that combines our orthogonal acquisition estimator with ensemble surrogates and an outer log transformation. We show theoretically that our estimator preserves the target, leads to variance reduction, and improves pairwise ranking stability. We further verify the theoretical properties of OrthoBO through numerical experiments where our framework reduces acquisition estimation variance, stabilizes candidate rankings, and achieves strong performance. We also demonstrate the downstream utility of OrthoBO in hyperparameter optimization for neural network training and fine-tuning.

Maresa Schröder, Pascal Janetzky, Michael Klar +1

LMU Munich · Munich Center for Machine Learning · Bosch Center for Artificial Intelligence

Bayesian OptimizationVariance ReductionHyperparameter Optimization
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May 7, 2026

Decoupled PFNs: Identifiable Epistemic-Aleatoric Decomposition via Structured Synthetic Priors

Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations. For sequential decision-making, such as active learning and Bayesian optimization, acquisition should prioritize epistemic uncertainty about the latent signal rather than irreducible aleatoric observation noise. We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone, even when that distribution is known exactly. We then exploit a distinctive advantage of PFNs: because the synthetic data-generating process is under our control, each task can contain an explicit latent signal and noise function, and the generator can provide query-level labels for both the noiseless target and the observation-noise variance. We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads. The observation-level predictive is induced by convolving the latent signal distribution with the learned noise model. Empirically, epistemic-only acquisition mitigates the failure mode of total-variance exploration in noisy and heteroscedastic settings. In matched comparisons, decoupled models usually improve over tuned observation-level baselines, with the clearest gains in HPO; in broader sweeps, a decoupled model obtains the best average rank in both HPO and synthetic BO.

Richard Bergna, Stefan Depeweg, José Miguel Hernández-Lobato

University of Cambridge · 2Siemens AG

Uncertainty QuantificationBayesian OptimizationActive LearningPrior-Data Fitted Networks
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May 7, 2026

In-Context Black-Box Optimization with Unreliable Feedback

Black-box optimization in science and engineering often comes with side information: experts, simulators, pretrained predictors, or heuristics can suggest which candidates look promising. This information can accelerate search, but it can also be biased, input-dependent, or misleading. Feedback-aware BO methods typically handle one task at a time, limiting their ability to generalize over multiple sources of feedback. In-context optimizers address cross-task adaptation, but usually assume that optimization history is the only available signal at test time. We study feedback-informed in-context black-box optimization (FICBO), where a pretrained optimizer conditions on both the observed history and cheap auxiliary feedback for the current candidate set. We introduce a structured feedback prior that models how feedback sources vary in their access, relevance, and distortion relative to the true objective, and use it to pretrain a feedback-aware transformer. At test time, the model estimates source reliability in context by comparing observed objective values with auxiliary signals, improving query selection. On synthetic and real-world tasks, FICBO effectively exploits informative feedback while remaining robust to weak or misleading sources, improving over other baselines. Empirical investigations further illustrate how the model perceives test-time sources, offering insights into its interpretability and decision-making process.

Nicolas Samuel Blumer, Julien Martinelli, Samuel Kaski

ELLIS Institute Finland · Aalto University · University of Manchester

Bayesian OptimizationBlack-Box OptimizationIn-Context Learning
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May 6, 2026

Meta-learning for sample-efficient Bayesian optimisation of fed-batch processes

The optimisation of fed-batch (bio)chemical process recipes is subject to inherent, underlying, and unmeasurable fluctuations across batches, whose trajectories are difficult to model and costly to measure. Bayesian Optimisation (BayesOpt) is a powerful tool for sampling and optimisation of expensive-to-measure functions. Gaussian Processes (GPs), the surrogate models used in BayesOpt, are static, forecast poorly, and lack generalisation across experiments, limiting their applicability to time-varying batch processes with stochastic parameters, i.e., process fluctuations. This work investigates System-Aware Neural ODE Processes (SANODEP) as a meta-learning model to overcome the limitations of GPs and increase few-shot optimisation performance in BayesOpt. Using a penicillin batch production case study, we find that SANODEP outperforms GP-based BayesOpt in the low-data regime, resulting in improved objectives when few experimental runs are performed. These improvements are observed in both on- and off-distribution batches, highlighting the generalisation capabilities of SANODEP. Using this approach, batch process operators can accelerate the initial optimisation steps in BayesOpt by deploying meta-learning or optimise the process with fewer experiments when the experimental cost is high.

Becky Langdon, Gabriel D. Patrón, Chrysoula D. Kappatou +6

Department of Computing, Imperial College London, United Kingdom · BASF SE, Ludwigshafen, Germany · School of Mathematical Sciences, Lancaster University, United Kingdom +1

Meta-LearningBayesian OptimizationNeural ODEs
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May 6, 2026

Regime-Conditioned Evaluation in Multi-Context Bayesian Optimization

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.

Noel Thomas

Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi, UAE

Causal Effect EstimationConditional Average Treatment Effect EstimationBayesian OptimizationBenchmark DesignSafe Bayesian OptimizationHyperparameter Optimization
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May 6, 2026

Elicitation Matters: How Prompts and Query Protocols Shape LLM Surrogates under Sparse Observations

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

Ge Lei, Samuel J. Cooper

Dyson School of Design Engineering Imperial College London Exhibition Road, London SW7 2AZ

Surrogate ModelingBayesian OptimizationLLM PromptingLarge Language Model-Guided OptimizationLLM Uncertainty Estimation
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May 4, 2026

Caliper-in-the-Loop: Black-Box Optimization for Hyperledger Fabric Performance Tuning

Hyperledger Fabric performance depends on many interacting configuration parameters, making manual tuning difficult. We study automated throughput tuning by treating benchmarking as a noisy black-box optimization problem and applying Bayesian optimization (BO) with dimensionality reduction (DR). We implement an end-to-end Caliper-in-the-loop pipeline that deploys candidate configurations, benchmarks them, and updates the optimizer from observed throughput. The search space, derived from Fabric configuration files, has 317 dimensions. In a cloud testbed, we evaluate 16 BO+DR variants and a random-search baseline. The best method, DYCORS-PCA, achieves a 12% TPS improvement relative to the first evaluated configuration, while MPI-REMBO achieves 9%. These results suggest that BO with DR is a practical approach for high-dimensional Hyperledger Fabric tuning, while also highlighting the role of measurement noise in interpreting gains.

Yash Madhwal, Arseny Bolotnikov, Mark Prikhno +5

Skolkovo Institute of Science and Technology, Moscow, Russia · HSE University, Moscow, Russia · Sberbank PJSC, Moscow, Russia +4

Bayesian OptimizationBlack-Box Optimization
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May 4, 2026

Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications

Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)

Sofianos Panagiotis Fotias, Vassilis Gaganis

School of Mining and Metallurgical Engineering, National Technical University of Athens, Athens, 15773, Greece

Bayesian OptimizationGaussian Processes
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Apr 30, 2026

Bayesian Optimization in Linear Time

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from 66 to 124124, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.

Jesse Schneider, William J. Welch

Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada

Bayesian OptimizationBlack-Box Optimization
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Apr 30, 2026

Human-in-the-Loop Meta Bayesian Optimization for Fusion Energy and Scientific Applications

Inertial Confinement Fusion (ICF) holds transformative promise for sustainable, near-limitless clean energy, yet remains constrained by prohibitively high costs and limited experimental opportunities. This paper presents Human-in-the-Loop Meta Bayesian Optimization (HL-MBO), a framework that integrates expert knowledge with few-shot, uncertainty-aware machine learning to accelerate discovery in data-scarce, high-stakes scientific domains. HL-MBO introduces a meta-learned surrogate model with an expert-informed acquisition function to recommend candidate experiments. To foster trust and enable informed decisions, HL-MBO also provides interpretable explanations of its suggestions. We show HL-MBO outperforms current BO methods on ICF energy yield optimization, as well as benchmarks in molecular optimization and critical temperature maximization for superconducting materials.

Ricardo Luna Gutierrez, Sahand Ghorbanpour, Ejaz Rahman +5

1Hewlett Packard Enterprise · University of Rochester

Meta-LearningBayesian OptimizationHuman-in-the-Loop AI
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Apr 28, 2026

Categorical Optimization with Bayesian Anchored Latent Trust Regions for Structural Design under High-Dimensional Uncertainty

Categorical structural optimization under aleatoric uncertainty is challenging because each design variable must be selected from a finite catalog of admissible instances, while each candidate design may require expensive stochastic finite-element evaluations. Existing latent-space optimization strategies can reduce the dimensionality of catalog attributes, but they often treat the reduced space as a continuous search domain. The resulting continuous optimum must then be rounded off to a nearby catalog instance, which may alter the objective value, constraint status, or physical interpretation of the design. To address this issue, this paper proposes the Categorical Optimization with Bayesian Anchored Latent Trust Regions (COBALT) framework for high-dimensional categorical Optimization Under Uncertainty. COBALT first embeds the physical catalog into a low-dimensional latent representation and locks the mapped instances as a discrete anchored graph. A data-independent random tree decomposition is then used to provide bounded-complexity additive modeling over high-dimensional categorical variables. On this anchored domain, an additive SAAS-GP surrogate is fitted to heteroscedastic MC-FEA observations, and a trust-region discrete graph acquisition search selects the next admissible catalog configuration without continuous relaxation or rounding-off. The proposed strategy is applied to robust design optimization of complex bar structures, considering structural weight, strain energy, and local buckling performance. By evaluating only valid catalog designs through the MC-FEA oracle, COBALT preserves physical admissibility throughout the active learning loop and improves the efficiency of robust categorical structural optimization.

Zhangyong Liang, Jie Hou, Huanhuan Gao +1

National Center for Applied Mathematics, Tianjin University, Weijin Road 92, 300072, Tianjin, China · School of Mechanical Engineering, Northwestern Polytechnical University, Youyixi Road 127, 710072, Xi’an, China · School of Mechanical and Aerospace Engineering, Jilin University, Renmin Street 5988, 130025, Changchun, China +1

Stochastic OptimizationSurrogate-Assisted OptimizationStructural MechanicsBayesian Optimization
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Apr 27, 2026

Feasible-First Exploration for Constrained ML Deployment Optimization in Crash-Prone Hierarchical Search Spaces

Deploying machine learning models under production constraints requires joint optimization over model family, quantization scheme, runtime backend, and serving configuration. This induces a hierarchical mixed-variable search space in which many configurations are invalid: evaluations may crash, exceed memory limits, or violate latency constraints. Standard black-box optimizers such as Tree-structured Parzen Estimators (TPE) and constrained Bayesian optimization are effective when valid configurations are common, but they can spend a large fraction of a small evaluation budget on invalid or uninformative trials in hostile deployment spaces. This paper studies that regime and asks whether optimization should be decomposed into an explicit exploration stage followed by model-guided exploitation. We propose Thermal Budget Annealing (TBA), a feasible-first exploration procedure that maps valid and feasible regions before warm-starting TPE. The method includes two robustness mechanisms for hostile hardware: trial timeouts that abort clearly infeasible evaluations early, and subspace blacklisting that temporarily suppresses categorical subspaces after repeated failures. We also introduce DeployBench, a benchmark suite for deployment optimization with hierarchical structure, hidden crash zones, hard constraints, and unequal evaluation costs. On synthetic benchmarks and real GPU deployment with five pre-trained vision models across five GPU targets (NVIDIA H100, A100, RTX 5080, L4, and T4), the proposed hybrid improves model-family discovery under tight constraints while reducing wasted budget relative to cold-start TPE.

Christian Lysenstøen

Department of Electrical Engineering and Computer Sciences University of California, Berkeley

Bayesian OptimizationBlack-Box OptimizationConstrained Optimization
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Apr 27, 2026

A Finite Time Analysis of Thompson Sampling for Bayesian Optimization with Preferential Feedback

Preference feedback, in the form of pairwise comparisons rather than scalar scores, has seen increasing use in applications such as human-, laboratory-, and expert-in-the-loop design, as well as scientific discovery. We propose a Thompson Sampling (TS) approach to Bayesian optimization with preferential feedback that models comparisons using a monotone link on latent utility differences and leverages the dueling kernel induced by a base kernel. We provide a finite-time analysis showing that the performance of the proposed method matches that of standard TS for conventional Bayesian optimization with scalar feedback. The analysis exploits the anchor invariance of TS for challenger selection and introduces a double-TS pairing variant. We also demonstrate the performance of the method on both synthetic and real-world examples.

Joseph Lazzaro, Davide Buffelli, Da-shan Shiu +1

Imperial College London · MediaTek Research

Thompson SamplingPairwise Preference EvaluationBayesian Optimization
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Apr 24, 2026

Rethinking Trust Region Bayesian Optimization in High Dimensions

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension DD and trust region side length LL vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Wei-Ting Tang, Joel A. Paulson

University of Wisconsin–Madison

Bayesian OptimizationBlack-Box OptimizationTrust-Region OptimizationGaussian Process Regression
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