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.

Latest papers

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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.

Apr 23, 2026

FLARE-BO: Fused Luminance and Adaptive Retinex Enhancement via Bayesian Optimisation for Low-Light Robotic Vision

Reliable visual perception under low illumination remains a core challenge for autonomous robotic systems, where degraded image quality directly compromises navigation, inspection, and various operations. A recent training free approach showed that Bayesian optimisation with Gaussian Processes can adaptively select brightness, contrast, and denoising parameters on a per-image basis, achieving competitive enhancement without any learned model. However, that framework is limited to three parameters, applies no illumination decomposition or white balance correction, and relies on Non-Local Means denoising, which tends to over smooth edges under noisy conditions. This paper proposes FLARE-BO (Fused Luminance and Adaptive Retinex Enhancement via Bayesian Optimisation), an extended framework that jointly optimises eight parameters spanning across gamma correction, LIME-style illumination normalisation, chrominance denoising, bilateral filtering, NLM denoising, Grey-World automatic white balance, and adaptive post smoothing. The search engine employs a unit hypercube parameter normalisation, objective standardisation, Sobol quasi-random initialisation, and Log Expected Improvement acquisition for principled exploration of the expanded space. Performance of the proposed method is benchmarked using the Low Light paired dataset (LOL) and results show marked improvements of the proposed method over existing methods that were not specifically trained using this dataset.

Nathan Shankar, Pawel Ladosz, Hujun Yin

Department of Mechanical, Aerospace and Civil Engineering and the Department of Electrical and Electronic Engineering at the University of Manchester, Manchester, M13 9PL, United Kingdom

Image EnhancementBayesian OptimizationLow-Light Image EnhancementRobotic Perception
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Apr 22, 2026

HARBOR: Automated Harness Optimization

Long-horizon language-model agents are dominated, in lines of code and in operational complexity, not by their underlying model but by the harness that wraps it: context compaction, tool caching, semantic memory, trajectory reuse, speculative tool prediction, and the glue that binds the model to a sandboxed execution environment. We argue that harness design is a first-class machine-learning problem and that automated configuration search dominates manual stacking once the flag space exceeds a handful of bits. We defend this claim in two steps. First, we formalize automated harness optimization as constrained noisy Bayesian optimization over a mixed-variable, cost-heterogeneous configuration space with cold-start-corrected rewards and a posterior chance-constrained safety check, and give a reference solver, HARBOR (Harness Axis-aligned Regularized Bayesian Optimization Routine), built from a block-additive SAAS surrogate, multi-fidelity cost-aware acquisition, and TuRBO trust regions. Second, we instantiate the problem in a flag-gated harness over a production coding agent and report a controlled four-round manual-tuning case study against a fixed task suite and an end-to-end HARBOR run. The formulation itself is task-class agnostic: the configuration space, reward correction, acquisition, and safety check apply to any agent harness with a bounded flag space and a reproducible task suite.

Biswa Sengupta, Jinhua Wang

LLM Suite Team, JP Morgan Chase & Co.

Bayesian OptimizationAgent Harness Optimization
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Apr 21, 2026

An Efficient Spatial Branch-and-Bound Algorithm for Global Optimization of Gaussian Process Posterior Mean Functions

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is challenging because it remains nonlinear and nonconvex. Existing exact deterministic approaches become increasingly difficult to scale as the number of training data points grows, leading to approximation-based methods that improve tractability by optimizing a modified (inexact) objective. In this work, we propose PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound. At each node, kernel terms that are locally important are replaced by a sign-aware piecewise-linear relaxation in an appropriate scalar distance variable, while the remaining terms are bounded analytically in closed form. We show this hybrid approach yields a valid lower bound for the posterior mean, while limiting the size of the branch-and-bound subproblems. We establish validity of the node lower bounds and ε\varepsilon-global convergence of the resulting algorithm. Computational results on synthetic benchmarks and real-world application problems show that PALM-Mean improves scalability relative to representative general-purpose deterministic global solvers, particularly as the number of training data points increases.

Wei-Ting Tang, Akshay Kudva, Calvin Tsay +1

Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, 53706, Wisconsin, USA. · Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruf Avenue, Columbus, 43210, Ohio, USA. · Department of Computing, Imperial College London, Exhibition Rd, South Kensington, SW7 2AZ, London, United Kingdom.

Bayesian OptimizationGlobal OptimizationGaussian Processes
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Apr 20, 2026

Collaborative Contextual Bayesian Optimization

Discovering optimal designs through sequential data collection is essential in many real-world applications. While Bayesian Optimization (BO) has achieved remarkable success in this setting, growing attention has recently turned to context-specific optimal design, formalized as Contextual Bayesian Optimization (CBO). Unlike BO, CBO is inherently more challenging as it must approximate an entire mapping from the context space to its corresponding optimal design, requiring simultaneous exploration across contexts and exploitation within each. In many modern applications, such tasks arise across multiple potentially heterogeneous but related clients, where collaboration can significantly improve learning efficiency. We propose CCBO, Collaborative Contextual Bayesian Optimization, a unified framework enabling multiple clients to jointly perform CBO with controllable contexts, supporting both online collaboration and offline initialization from peers' historical beliefs, with an optional privacy-preserving communication mechanism. We establish sublinear regret guarantees and demonstrate, through extensive simulations and a real-world hot rolling application, that CCBO achieves substantial improvements over existing approaches even under client heterogeneity. The code to reproduce the results can be found at https://github.com/cchihyu/Collaborative-Contextual-Bayesian-Optimization

Chih-Yu Chang, Qiyuan Chen, Tianhan Gao +5

Department of Mathematics, Imperial College London, London, United Kingdom · Department of Industrial & Operations Engineering, University of Michigan, Ann Arbor, MI, USA · Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA +1

Bayesian Optimization
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Apr 20, 2026

QuickScope: Certifying Hard Questions in Dynamic LLM Benchmarks

LLM benchmarks are increasingly dynamic: instead of containing a fixed set of questions, they define templates and parameters that can generate an effectively unlimited number of question variants. This flexibility is valuable, but it makes evaluation expensive -- especially when the goal is not just determining an average score, but reliably identifying a model's weak spots. This paper introduces a new methodology for identifying hard questions in dynamic benchmarks. It leverages COUP, a recent Bayesian optimization algorithm (Graham, Velez & Leyton-Brown, 2026), after introducing several substantive modifications to make the algorithm suitable for practical LLM pipelines. We also wrap it in a tool that supports flexible choices of datasets and utility functions, enabling users to target the kinds of questions they care about (e.g., low-accuracy questions; questions that are unusually hard relative to their measured complexity). In experiments across a range of benchmarks, we show that our method, dubbed QuickScope\texttt{QuickScope}, discovers truly difficult questions more sample efficiently than standard baselines, while also reducing false positives from noisy outcomes.

Taylor Lundy, Narun K. Raman, Kevin Leyton-Brown

Department of Computer Science University of British Columbia Vancouver, BC

LLM EvaluationBayesian OptimizationBenchmark Design
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Apr 19, 2026

SLO-Guard: Crash-Aware, Budget-Consistent Autotuning for SLO-Constrained LLM Serving

Serving large language models under latency service-level objectives (SLOs) is a configuration-heavy systems problem with an unusually failure-prone search space: many plausible configurations crash outright or miss user-visible latency targets, and standard black-box optimizers treat these failures as wasted trials. We present SLO-Guard, a crash-aware autotuner for vLLM serving that treats crashes as first-class observations. SLO-Guard combines a feasible-first Thermal Budget Annealing (TBA) exploration phase with a warm-started Tree-structured Parzen Estimator (TPE) exploitation phase; the handoff replays all exploration history, including crashes encoded as extreme constraint violations. We additionally contribute a configuration-repair pass, a GPU-aware KV-cache memory guard, and a four-category crash taxonomy. We evaluate SLO-Guard on Qwen2-1.5B served with vLLM 0.19 on an NVIDIA A100 40GB. Across a pre-specified five-seed study, both SLO-Guard and uniform random search attain 75/75 feasibility with zero crashes under the corrected concurrent harness, and are statistically tied on best-achieved latency (Mann-Whitney two-sided p=0.84). SLO-Guard's advantage is in budget consistency: more trials in the fast-serving regime (10.20 vs. 7.40 out of 15; one-sided p=0.014) and higher post-handoff consistency (0.876 vs. 0.539; p=0.010). Under concurrent load, SLO-Guard's cross-seed standard deviation on best latency is 4.4x tighter than random search's (2.26 ms vs. 10.00 ms). A harness-replication analysis shows that the consistency findings survive an independent sequential-dispatch measurement condition. The central claim is not that SLO-Guard finds a better final configuration, but that it spends a fixed tuning budget more predictably once the fast regime has been found.

Christian Lysenstøen

Inland Norway University of Applied Sciences · Visiting Student, University of California, Berkeley

LLM Inference EfficiencyLLM ServingBayesian OptimizationBlack-Box Optimization
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Apr 17, 2026

Multi-Objective Bayesian Optimization via Adaptive \varepsilon-Constraints Decomposition

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling ε\varepsilon-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in ε\varepsilon-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

Yaohong Yang, Sammie Katt, Samuel Kaski

Department of Computer Science, Aalto University, Espoo, Finland · ELLIS Institute Finland · Department of Computer Science, University of Manchester, Manchester, United Kingdom

Bayesian OptimizationMulti-Objective Optimization
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Apr 15, 2026

BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization

Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our `plug-and-play' framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.

Jackie Rao, Ferran Gonzalez Hernandez, Leon Gerard +1

MRC Biostatistics Unit, University of Cambridge, UK · Centre for AI, Data Science and Artificial Intelligence, R&D, AstraZeneca, Barcelona, Spain

Protein DesignSurrogate-Assisted OptimizationBayesian OptimizationMolecular GenerationEvolutionary Optimization
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Apr 15, 2026

Optimization with SpotOptim

The spotoptim package implements surrogate-model-based optimization of expensive black-box functions in Python. Building on two decades of Sequential Parameter Optimization (SPO) methodology, it provides a Kriging-based optimization loop with Expected Improvement, support for continuous, integer, and categorical variables, noise-aware evaluation via Optimal Computing Budget Allocation (OCBA), and multi-objective extensions. A success-rate-based restart mechanism detects stagnation while preserving the best solution found. The package returns scipy-compatible OptimizeResult objects and accepts any scikit-learn-compatible surrogate model. Built-in TensorBoard logging provides real-time monitoring of convergence and surrogate quality. This report describes the architecture and module structure of spotoptim, provides worked examples including neural network hyperparameter tuning, and compares the framework with BoTorch, Optuna, RayTune, BOHB, SMAC, and Hyperopt. The package is open-source (AGPL-3.0).

Thomas Bartz-Beielstein

Bartz & Bartz GmbH, 51643 Gummersbach, Germany

Black-Box OptimizationSurrogate-Assisted OptimizationBayesian OptimizationHyperparameter Optimization
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Apr 13, 2026

BayMOTH: Bayesian optiMizatiOn with meTa-lookahead -- a simple approacH

Bayesian optimization (BO) has for sequential optimization of expensive black-box functions demonstrated practicality and effectiveness in many real-world settings. Meta-Bayesian optimization (meta-BO) focuses on improving the sample efficiency of BO by making use of information from related tasks. Although meta-BO is sample-efficient when task structure transfers, poor alignment between meta-training and test tasks can cause suboptimal queries to be suggested during online optimization. To this end, we propose a simple meta-BO algorithm that utilizes related-task information when determined useful, falling back to lookahead otherwise, within a unified framework. We demonstrate competitiveness of our method with existing approaches on function optimization tasks, while retaining strong performance in low task-relatedness regimes where test tasks share limited structure with the meta-training set.

Rahman Ejaz, Varchas Gopalaswamy, Ricardo Luna +5

Laboratory for Laser Energetics, Rochester, NY, USA · Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA · Hewlett Packard Labs, Santa Clara, CA, USA +2

Bayesian OptimizationMulti-Task Optimization
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Apr 10, 2026

Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?

Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire Pareto front typically grows substantially. This makes it challenging, if not infeasible, to design a search algorithm capable of effectively exploring the entire Pareto front. This difficulty is particularly acute in the Bayesian optimisation paradigm, where sample efficiency is critical and only a limited number of solutions (often a few hundred) are evaluated. Moreover, after the optimisation process, the decision-maker eventually selects just one solution for deployment, regardless of how many high-quality, diverse solutions are available. In light of this, we argue an idea that under a very limited evaluation budget, it may be more useful to focus on finding a single solution of the highest possible quality for the decision-maker, rather than aiming to approximate the entire Pareto front as existing many-/multi-objective Bayesian optimisation methods typically do. Bearing this idea in mind, this paper proposes a single point-based multi-objective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within SPMO, we present a simple acquisition function, called expected single-point improvement (ESPI), working under both noiseless and noisy scenarios. We show that ESPI can be optimised effectively with gradient-based methods via the sample average approximation (SAA) approach and theoretically prove its convergence guarantees under the SAA. We also empirically demonstrate that the proposed SPMO is computationally tractable and outperforms state-of-the-arts on a wide range of benchmark and real-world problems.

Chao Jiang, Jingyu Huang, Miqing Li

School of Computer Science, University of Birmingham · School of Mathematics, University of Birmingham

Multi-Objective OptimizationBayesian Optimization
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Apr 10, 2026

Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization

In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods -- including those that use trust regions or other local approximations -- producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.

Donney Fan, Geoff Pleiss

University of British Columbia Vector Institute

Bayesian OptimizationThompson SamplingAdaptive Sampling
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Apr 8, 2026

Bayesian Optimization for Mixed-Variable Problems in the Natural Sciences

Optimizing expensive black-box objectives over mixed search spaces is a common challenge across the natural sciences. Bayesian optimization (BO) offers sample-efficient strategies through probabilistic surrogate models and acquisition functions. However, its effectiveness diminishes in mixed or high-cardinality discrete spaces, where gradients are unavailable and optimizing the acquisition function becomes computationally demanding. In this work, we generalize the probabilistic reparameterization (PR) approach of Daulton et al. to handle non-equidistant discrete variables, enabling gradient-based optimization in fully mixed-variable settings with Gaussian process (GP) surrogates. With real-world scientific optimization tasks in mind, we conduct systematic benchmarks on synthetic and experimental objectives to obtain an optimized kernel formulations and demonstrate the robustness of our generalized PR method. We additionally show that, when combined with a modified BO workflow, our approach can efficiently optimize highly discontinuous and discretized objective landscapes. This work establishes a practical BO framework for addressing fully mixed optimization problems in the natural sciences, and is particularly well suited to autonomous laboratory settings where noise, discretization, and limited data are inherent.

Yuhao Zhang, Ti John, Matthias Stosiek +1

Department of Applied Physics, Aalto University, Puumiehenkuja 2, Espoo, 02320, Finland · School of Natural Sciences Physics Department, Technical University of Munich, James-Franck-Str. 1, Garching bei München, 85748, Germany · Atomistic Modeling Center, Munich Data Science Institute, Technical University of Munich, Walther-von-Dyck Str. 10, Garching bei München, 85748, Germany +1

Bayesian Optimization
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Apr 7, 2026

Multi-Agent Pathfinding with Non-Unit Integer Edge Costs via Enhanced Conflict-Based Search and Graph Discretization

Multi-Agent Pathfinding (MAPF) plays a critical role in various domains. Traditional MAPF methods typically assume unit edge costs and single-timestep actions, which limit their applicability to real-world scenarios. MAPFR extends MAPF to handle non-unit costs with real-valued edge costs and continuous-time actions, but its geometric collision model leads to an unbounded state space that compromises solver efficiency. In this paper, we propose MAPFZ, a novel MAPF variant on graphs with non-unit integer costs that preserves a finite state space while offering improved realism over classical MAPF. To solve MAPFZ efficiently, we develop CBS-NIC, an enhanced Conflict-Based Search framework incorporating time-interval-based conflict detection and an improved Safe Interval Path Planning (SIPP) algorithm. Additionally, we propose Bayesian Optimization for Graph Design (BOGD), a discretization method for non-unit edge costs that balances efficiency and accuracy with a sub-linear regret bound. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods in runtime and success rate across diverse benchmark scenarios.

Hongkai Fan, Qinjing Xie, Bo Ouyang +4

College of Electrical and Information Engineering at Hunan University · China Mobile Group Hunan Company Limited, Changsha 410082, China

Safe Interval Path PlanningMulti-Agent Path FindingConflict-Based SearchBayesian Optimization
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Apr 2, 2026

Preferential Bayesian Optimization with Crash Feedback

Bayesian optimization is a popular black-box optimization method for parameter learning in control and robotics. It typically requires an objective function that reflects the user's optimization goal. However, in practical applications, this objective function is often inaccessible due to complex or unmeasurable performance metrics. Preferential Bayesian optimization (PBO) overcomes this limitation by leveraging human feedback through pairwise comparisons, eliminating the need for explicit performance quantification. When applying PBO to hardware systems, such as in quadcopter control, crashes can cause time-consuming experimental resets, wear and tear, or otherwise undesired outcomes. Standard PBO methods cannot incorporate feedback from such crashed experiments, resulting in the exploration of parameters that frequently lead to experimental crashes. We thus introduce CrashPBO, a user-friendly mechanism that enables users to both express preferences and report crashes during the optimization process. Benchmarking on synthetic functions shows that this mechanism reduces crashes by 63% and increases data efficiency. Through experiments on three robotics platforms, we demonstrate the wide applicability and transferability of CrashPBO, highlighting that it provides a flexible, user-friendly framework for parameter learning with human feedback on preferences and crashes.

Johanna Menn, David Stenger, Sebastian Trimpe

Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University, Aachen, Germany · aiXopt GmbH, Aachen, Germany

Bayesian OptimizationSafe Bayesian Optimization
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Apr 1, 2026

Efficient and Principled Scientific Discovery through Bayesian Optimization: A Tutorial

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.

Zhongwei Yu, Rasul Tutunov, Alexandre Max Maraval +13

The Hong Kong University of Science and Technology (Guangzhou) · Huawei Noah’s Ark Lab · University of Science and Technology of China +5

Bayesian OptimizationScientific DiscoveryBayesian Experimental DesignAutonomous Experimentation
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Apr 1, 2026

Safe learning-based control via function-based uncertainty quantification

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward and constraint functions or the underlying dynamics model, with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions that encode smoothness properties of the unknown function, such as a known norm in a function space. Moreover, these methods usually struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated. We then construct uncertainty tubes via the scenario approach that hold with high probability. Our uncertainty tubes rely solely on sampled realizations and can therefore accommodate discontinuities represented by the sampling model. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm with which we safely tune control parameters on a real Furuta pendulum.

Abdullah Tokmak, Toni Karvonen, Thomas B. Schön +1

Cyber-physical Systems Group, Aalto University, Espoo, Finland · School of Engineering Sciences, Lappeenranta–Lahti University of Technology LUT, Lappeenranta, Finland · Department of Information Technology, Uppsala University, Uppsala, Sweden

Uncertainty QuantificationSafety-Critical ControlBayesian OptimizationSafe Bayesian Optimization
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Mar 31, 2026

mlr3mbo: Bayesian Optimization in R

We present mlr3mbo, a modular toolbox for Bayesian optimization in R. mlr3mbo supports single- and multi-objective optimization, multi-point proposals, batch and asynchronous parallelization, and robust error handling. While it can be used for many standard Bayesian optimization variants in applied settings, researchers can also construct custom Bayesian optimization algorithms from its flexible building blocks. In addition to an introduction to the software, its design principles, and its building blocks, the paper presents two extensive empirical evaluations on the surrogate-based benchmark suite YAHPO Gym. To identify robust default configurations for both numeric and mixed-hierarchical optimization regimes, and to gain further insights into the respective impacts of individual settings, we run a coordinate descent search over the mlr3mbo configuration space and analyze its results. Furthermore, we benchmark mlr3mbo against a wide range of established optimizers, including HEBO, SMAC3, Ax, and Optuna, and find that it performs on par with state-of-the-art.

Marc Becker, Lennart Schneider, Martin Binder +2

Department of Statistics, LMU Munich, Munich, Germany · Munich Center for Machine Learning (MCML), Munich, Germany · University of St Andrews, St Andrews, Scotland

Bayesian OptimizationHyperparameter Optimization
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Mar 30, 2026

Transfer Learning in Bayesian Optimization for Aircraft Design

The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called cold start problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a meta data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.

Ali Tfaily, Youssef Diouane, Nathalie Bartoli +1

1*Department of Mechanical Engineering, McGill University, Canada. · 2Advanced Product Development, Bombardier, Canada. · Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Canada. +4

Bayesian OptimizationSurrogate-Assisted OptimizationConstrained Optimization
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Mar 30, 2026

Multi-Agent LLMs for Adaptive Acquisition in Bayesian Optimization

The exploration-exploitation trade-off is central to sequential decision-making and black-box optimization, yet how Large Language Models (LLMs) reason about and manage this trade-off remains poorly understood. Unlike Bayesian Optimization, where exploration and exploitation are explicitly encoded through acquisition functions, LLM-based optimization relies on implicit, prompt-based reasoning over historical evaluations, making search behavior difficult to analyze or control. In this work, we present a metric-level study of LLM-mediated search policy learning, studying how LLMs construct and adapt exploration-exploitation strategies under multiple operational definitions of exploration, including informativeness, diversity, and representativeness. We show that single-agent LLM approaches, which jointly perform strategy selection and candidate generation within a single prompt, suffer from cognitive overload, leading to unstable search dynamics and premature convergence. To address this limitation, we propose a multi-agent framework that decomposes exploration-exploitation control into strategic policy mediation and tactical candidate generation. A strategy agent assigns interpretable weights to multiple search criteria, while a generation agent produces candidates conditioned on the resulting search policy defined as weights. This decomposition renders exploration-exploitation decisions explicit, observable, and adjustable. Empirical results across various continuous optimization benchmarks indicate that separating strategic control from candidate generation substantially improves the effectiveness of LLM-mediated search.

Andrea Carbonati, Mohammadsina Almasi, Hadis Anahideh

University of Illinois Chicago, IL, USA

Large Language Model-Guided OptimizationExploration-Exploitation TradeoffMulti-Agent LLMsPolicy LearningBayesian Optimization
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Mar 30, 2026

Active Preference Learning over Latent Preference Archetypes for Many-Objective Bayesian Optimization

Preference-based many-objective Bayesian optimization typically assumes that all pairwise comparisons arise from a single latent utility function, despite real decision makers often exhibiting multiple latent preference archetypes across contexts. We propose an active preference learning framework for many-objective Bayesian optimization that infers latent preference archetypes from pairwise comparisons, enabling both the identification of the active trade-off strategy and the refinement of its associated preferences. Our framework represents preferences as a Dirichlet-process mixture of latent archetypes and introduces mixture-aware information-theoretic query strategies that separately target archetype identification and within-archetype refinement through a hybrid acquisition policy. Experiments on synthetic benchmarks and real-world chemical process design case-study consistently outperforms state-of-the-art preference-based Bayesian optimization methods while recovering interpretable latent preference structure beyond conventional single-utility models. The proposed mixture-aware diagnostics further quantify archetype recovery and preference calibration, providing insights that are not captured by optimization performance alone.

Manisha Dubey, Sebastiaan De Peuter, Wanrong Wang +1

Department of Computer Science, University of Manchester, UK · Centre for AI in Assistive Autonomy, University of Edinburgh, Scotland, UK · Department of Computer Science, Aalto University, Espoo, Finland +2

Active Preference LearningBayesian OptimizationPreference LearningMulti-Objective OptimizationPairwise Preference Learning
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Mar 27, 2026

Optimal Transport-based Permutation-Invariant Bayesian Optimization of Offshore Wind Farm Layouts

Bayesian Optimization (BO) is widely and successfully adopted for solving optimization problems having an expensive-to-evaluate, black-box, and non-convex objective function. However, the vanilla BO algorithm is not able to exploit possible symmetries characterizing the target problem. An intuitive case is given by optimal location problems, whose decision variables refer to a finite set of points within a continuous space, with the order of points not affecting the value of the objective function. We refer to this setting as optimization over layouts to distinguish from optimization over point-clouds where, instead, the order of points counts. As an instance of optimization over layouts we consider a real-life industrial-relevant application, that is the optimization of the layout of an offshore wind farm: given identical wind turbines, switching any pair of them has not any effect on the annual energy production. Based on Optimal Transport theory, we propose a Permutation-Invariant BO approach, namely PIBO, proved to provide better wind farm layouts when compared to the vanilla BO approach while cutting computation time roughly in half.

Antonio Candelieri, Laurens Bliek

Department of Economics Management and Statistics, University of Milano-Bicocca, Milan, Italy. · Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven, the Netherlands. · Eindhoven AI Systems Institute, Eindhoven, the Netherlands.

Bayesian Optimization
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Mar 27, 2026

Curvature-aware Expected Free Energy as an Acquisition Function for Bayesian Optimization

We propose an Expected Free Energy-based acquisition function for Bayesian optimization to solve the joint learning and optimization problem, i.e., optimize and learn the underlying function simultaneously. We show that, under specific assumptions, Expected Free Energy reduces to Upper Confidence Bound, Lower Confidence Bound, and Expected Information Gain. We prove that Expected Free Energy has unbiased convergence guarantees for concave functions. Using the results from these derivations, we introduce a curvature-aware update law for Expected Free Energy and show its proof of concept using a system identification problem on a Van der Pol oscillator. On a two-dimensional benchmark with an oscillatory landscape, our adaptive Expected Free Energy acquisition achieves competitive performance in both regret and mean squared error, unlike the typical acquisition functions that perform well in only one metric.

Ajith Anil Meera, Wouter Kouw

Faculty of Electrical Engineering, TU Eindhoven, The Netherlands

Free Energy CalculationBayesian OptimizationBayesian Experimental DesignExpected Free Energy
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Mar 26, 2026

Practical Efficient Global Optimization is No-regret

Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization algorithms.It comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO is applied, a scalar matrix of a small positive value (also called a nugget or jitter) is usually added to the covariance matrix of the deterministic GP to improve numerical stability. We refer to this EGO with a positive nugget as the practical EGO. Despite its wide adoption and empirical success, to date, cumulative regret bounds for practical EGO have yet to be established. In this paper, we present for the first time the cumulative regret upper bound of practical EGO. In particular, we show that practical EGO has sublinear cumulative regret bounds and thus is a no-regret algorithm for commonly used kernels including the squared exponential (SE) and Matérn kernels (ν>12ν>\frac{1}{2}). Moreover, we analyze the effect of the nugget on the regret bound and discuss the theoretical implication on its choice. Numerical experiments are conducted to support and validate our findings.

Jingyi Wang, Haowei Wang, Nai-Yuan Chiang +3

Lawrence Livermore National Laboratory, CA, USA · National University of Singapore, Singapore · National Laboratory of the Rockies, CO, USA

Bayesian OptimizationGlobal OptimizationRegret Minimization
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Mar 25, 2026

Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions

Traffic simulation and digital-twin calibration is a challenging optimization problem with a limited simulation budget. Each trial requires an expensive simulation run, and the relationship between calibration inputs and model error is often nonconvex, and noisy. The problem becomes more difficult as the number of calibration parameters increases. We compare a commonly used automatic calibration method, a genetic algorithm (GA), with Bayesian optimization methods (BOMs): classical Bayesian optimization (BO), Trust-Region BO (TuRBO), Multi-TuRBO, and a proposed Memory-Guided TuRBO (MG-TuRBO) method. We compare performance on 2 real-world traffic simulation calibration problems with 14 and 84 decision variables, representing lower- and higher-dimensional (14D and 84D) settings. For BOMs, we study two acquisition strategies, Thompson sampling and a novel adaptive strategy. We evaluate performance using final calibration quality, convergence behavior, and consistency across runs. The results show that BOMs reach good calibration targets much faster than GA in the lower-D problem. MG-TuRBO performs comparably in our 14D setting, it demonstrates noticeable advantages in the 84D problem, particularly when paired with our adaptive strategy. Our results suggest that MG-TuRBO is especially useful for high-D traffic simulation calibration and potentially for high-D problems in general.

Abhilasha Saroj, Shaked Regev, Guanhao Xu +3

Bayesian OptimizationBlack-Box OptimizationTrust-Region Optimization
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Mar 25, 2026

Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling

Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that combines a penalty formulation, a surrogate model, and a trust region strategy. The constrained problem is converted to an unconstrained form by penalizing constraint violations, which provides a unified modeling framework. A trust region restricts the search to a local region around the current best solution, which improves stability and efficiency in high dimensions. Within this region, we use the Expected Improvement acquisition function to select evaluation points by balancing improvement and uncertainty. The proposed Trust Region method integrates penalty-based constraint handling with local surrogate modeling. This combination enables efficient exploration of feasible regions while maintaining sample efficiency. We compare the proposed method with state-of-the-art methods on synthetic and real-world high-dimensional constrained optimization problems. The results show that the method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance across different settings.

Raju Chowdhury, Tanmay Sen, Biswabrata Pradhan

Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, Kolkata, India.

Bayesian OptimizationBlack-Box OptimizationSurrogate-Assisted OptimizationTrust-Region Optimization
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Mar 25, 2026

Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models

Tuning control policies manually to meet high-level objectives is often time-consuming. Bayesian optimization provides a data-efficient framework for automating this process using numerical evaluations of an objective function. However, many systems, particularly those involving humans, require optimization based on subjective criteria. Preferential Bayesian optimization addresses this by learning from pairwise comparisons instead of quantitative measurements, but relying solely on preference data can be inefficient. We propose a multi-fidelity, multi-modal Bayesian optimization framework that integrates low-fidelity numerical data with high-fidelity human preferences. Our approach employs Gaussian process surrogate models with both hierarchical, autoregressive and non-hierarchical, coregionalization-based structures, enabling efficient learning from mixed-modality data. We illustrate the framework by tuning an autonomous vehicle's trajectory planner, showing that combining numerical and preference data significantly reduces the need for experiments involving the human decision maker while effectively adapting driving style to individual preferences.

Lukas Theiner, Maik Pfefferkorn, Yongpeng Zhao +2

Control and Cyber-Physical Systems Laboratory, Technical University of Darmstadt, Darmstadt, Germany · Volkswagen AG, Wolfsburg, Germany

Bayesian OptimizationMulti-Fidelity OptimizationSurrogate Modeling
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Mar 22, 2026

ALMAB-DC: Active Learning, Multi-Armed Bandits, and Distributed Computing for Sequential Experimental Design and Black-Box Optimization

Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose ALMAB-DC, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at K=4K=4 the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4% CIFAR-10 accuracy (outperforming BOHB by 1.7,pp and Optuna by 1.1,pp), reduces airfoil drag to CD=0.059C_D = 0.059 (36.9% below Grid Search), and improves RL return by 50% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney UU tests. Distributed execution achieves 7.5×7.5\times speedup at K=16K = 16 agents, consistent with Amdahl's Law.

Foo Hui-Mean, Yuan-chin I Chang

Institute of Statistical Science, Academia Sinica, Taipei, Taiwan

Sequential Experimental DesignActive Experimental DesignBayesian OptimizationBayesian Experimental DesignActive LearningMulti-Armed Bandits
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Mar 20, 2026

ReBOL: Retrieval via Bayesian Optimization with Batched LLM Relevance Observations and Query Reformulation

LLM-reranking is limited by the top-k documents retrieved by vector similarity, which neither enables contextual query-document token interactions nor captures multimodal relevance distributions. While LLM query reformulation attempts to improve recall by generating improved or additional queries, it is still followed by vector similarity retrieval. We thus propose to address these top-k retrieval stage failures by introducing ReBOL, which 1) uses LLM query reformulations to initialize a multimodal Bayesian Optimization (BO) posterior over document relevance, and 2) iteratively acquires document batches for LLM query-document relevance scoring followed by posterior updates to optimize relevance. After exploring query reformulation and document batch diversification techniques, we evaluate ReBOL against LLM reranker baselines on five BEIR datasets and using two LLMs (Gemini-2.5-Flash-Lite, GPT-5.2). ReBOL consistently achieves higher recall and competitive rankings, for example compared to the best LLM reranker on the Robust04 dataset with 46.5% vs. 35.0% recall@100 and 63.6% vs. 61.2% NDCG@10. We also show that ReBOL can achieve comparable latency to LLM rerankers.

Anton Korikov, Scott Sanner

University of Toronto

Information RetrievalLLM RerankingMultimodal IRBayesian Optimization
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Mar 19, 2026

Self-Tuning Sparse Attention: Multi-Fidelity Hyperparameter Optimization for Transformer Acceleration

Sparse attention mechanisms promise to break the quadratic bottleneck of long-context transformers, yet production adoption remains limited by a critical usability gap: optimal hyperparameters vary substantially across layers and models, and current methods (e.g., SpargeAttn) rely on manual grid search to identify them. We propose AFBS-BO (Adaptive Fidelity Binary Search with Bayesian Optimization), a fully automated framework that discovers optimal layer- and head-specific hyperparameters without human intervention. Our hybrid algorithm combines Bayesian Optimization for global exploration with binary search for local refinement, leveraging multi-fidelity evaluation across sequence lengths to reduce tuning cost. On Llama-2-7B, AFBS-BO accelerates hyperparameter discovery by 3.4x with 8.8x fewer evaluations than grid search, and identifies high-sparsity configurations that outperform existing sparse attention baselines while closely matching dense attention quality. By transforming sparse attention from a manually tuned heuristic into a self-optimizing primitive, AFBS-BO enables plug-and-play acceleration across diverse transformer architectures and domains.

Arundhathi Dev, Justin Zhan

Department of Computer Science, University of Cincinnati, Cincinnati, USA

Sparse AttentionHyperparameter OptimizationMulti-Fidelity OptimizationBayesian Optimization
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