Bayesian optimization (BO) is a sequential decision-making tool widely used for optimizing expensive black-box functions. Recently, Large Language Models (LLMs) have shown remarkable adaptability in low-data regimes, making them promising tools for black-box optimization by leveraging contextual knowledge to propose high-quality query points. However, LLMs lack explicit surrogate modeling and calibrated uncertainty, and their internal mechanisms remain opaque. This structural opacity can result in unnecessary experiments, which are costly in BO and may prevent the search from approaching the optimum. To address this, we propose LLINBO: LLM-in-the-Loop BO, a general framework that wraps existing LLM-based BO approaches, deciding when and how to act on their suggestions and when to revert to classical BO. We introduce three mechanisms for this interaction, each accompanied by a no-harm theoretical guarantee that ensures sublinear cumulative regret for common kernels while requiring no performance assumptions on the LLM. Beyond these theoretical guarantees, we show through simulation studies that LLINBO makes existing LLM-based BO more reliable while still exploiting the LLM's few-shot learning ability to outperform classical BO. We further demonstrate its practical use on a real-world, expensive 3D printing experiment. Code is available at https://github.com/UMDataScienceLab/LLM-in-the-Loop-BO.
Bayesian optimization of function networks (BOFN) is a framework for optimizing expensive-to-evaluate objective functions structured as networks, where some nodes' outputs serve as inputs for others. Many real-world applications, such as manufacturing and drug discovery, involve function networks with additional properties - nodes that can be evaluated independently and incur varying costs. A recent BOFN variant, p-KGFN, leverages this structure and enables cost-aware partial evaluations, selectively querying only a subset of nodes at each iteration. p-KGFN reduces the number of expensive objective function evaluations needed but has a large computational overhead: choosing where to evaluate requires optimizing a nested Monte Carlo-based acquisition function for each node in the network. To address this, we propose an accelerated p-KGFN algorithm that reduces computational overhead with only a modest loss in query efficiency. Key to our approach is generation of node-specific candidate inputs for each node in the network via one inexpensive global Monte Carlo simulation. Numerical experiments show that our method maintains competitive query efficiency while achieving up to a 16x speedup over the original p-KGFN algorithm.
Traditional wind farm control operates each turbine independently to maximize individual power output. However, coordinated wake steering across the entire farm can substantially increase the combined wind farm energy production. Although dynamic closed-loop control has proven effective in flow control applications, wind farm optimization has relied primarily on static, low-fidelity simulators that ignore critical turbulent flow dynamics. In this work, we present the first reinforcement learning (RL) controller integrated directly with high-fidelity large-eddy simulation (LES), enabling real-time response to atmospheric turbulence through collaborative, dynamic control strategies. Our RL controller achieves a 4.30% increase in wind farm power output compared to baseline operation, nearly doubling the 2.19% gain from static optimal yaw control obtained through Bayesian optimization. These results establish dynamic flow-responsive control as a transformative approach to wind farm optimization, with direct implications for accelerating renewable energy deployment to net-zero targets.
Hybrid quantum-classical machine learning offers a path to leverage noisy intermediate-scale quantum (NISQ) devices for drug discovery, but optimal model architectures remain unclear. We systematically optimize the quantum-classical bridge architecture for generative adversarial networks (GANs) in molecular discovery using multi-objective Bayesian optimization. Our optimized model (BO-QGAN) significantly improves performance, achieving a 2.27-fold higher Drug Candidate Score (DCS) than prior quantum-hybrid benchmarks and 2.21-fold higher than the classical baseline, using over 60% fewer parameters. Key findings favor layering multiple (3-4) shallow (4-8 qubit) quantum circuits sequentially, while classical architecture shows less sensitivity above a minimum capacity. This work provides the first empirically grounded architectural guidelines for hybrid models, enabling more effective integration of current quantum computers into pharmaceutical research pipelines.
Bayesian optimization (BO) is a powerful class of algorithms for optimizing expensive black-box functions, but designing effective BO algorithms remains a manual, expertise-driven task. Recent advancements in Large Language Models (LLMs) have opened new avenues for automating scientific discovery, including the automatic design of optimization algorithms. While prior work has used LLMs within optimization loops or to generate non-BO algorithms, we tackle a new challenge: Using LLMs to automatically generate full BO algorithm code. Our framework uses an evolution strategy to guide an LLM in generating Python code that preserves the key components of BO algorithms: An initial design, a surrogate model, and an acquisition function. The LLM is prompted to produce multiple candidate algorithms, which are evaluated on the established Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) platform. Based on their performance, top candidates are selected, combined, and mutated via controlled prompt variations, enabling iterative refinement. Despite no additional fine-tuning, the LLM-generated algorithms outperform state-of-the-art BO baselines in 19 (out of 24) BBOB functions in dimension 5 and generalize well to higher dimensions, and different tasks (from the Bayesmark framework). This work demonstrates that LLMs can serve as algorithmic co-designers, offering a new paradigm for automating BO development and accelerating the discovery of novel algorithmic combinations. The source code is provided at https://github.com/Ewendawi/LLaMEA-BO.
The expressiveness of flow-based models combined with stochastic variational inference (SVI) has, in recent years, expanded the application of optimization-based Bayesian inference to include problems with complex data relationships. However, until now, SVI using flow-based models has been limited to problems of fixed dimension. We introduce CoSMIC, normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables using a single amortized variational density for inference over a transdimensional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using techniques from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments demonstrate the performance of VTI on challenging problems that scale to high-cardinality model spaces.
Developing machine learning (ML) models requires a deep understanding of real-world problems, which are inherently multi-objective. In this paper, we present VirnyFlow, the first design space for responsible model development, designed to assist data scientists in building ML pipelines that are tailored to the specific context of their problem. Unlike conventional AutoML frameworks, VirnyFlow enables users to define customized optimization criteria, perform comprehensive experimentation across pipeline stages, and iteratively refine models in alignment with real-world constraints. Our system integrates evaluation protocol definition, multi-objective Bayesian optimization, cost-aware multi-armed bandits, query optimization, and distributed parallelism into a unified architecture. We show that VirnyFlow significantly outperforms state-of-the-art AutoML systems in both optimization quality and scalability across five real-world benchmarks, offering a flexible, efficient, and responsible alternative to black-box automation in ML development.
Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in high-dimensional search spaces or when lacking domain-specific priors, leading to sparse or uninformative suggestions. To overcome these limitations, we propose HOLLM, a novel global optimization algorithm that enhances LLM-driven sampling by partitioning the search space into promising subregions. Each subregion acts as a ``meta-arm'' selected via a bandit-inspired scoring mechanism that effectively balances exploration and exploitation. Within each selected subregion, an LLM then proposes high-quality candidate points, without any explicit domain knowledge. Empirical evaluation on standard optimization benchmarks shows that HOLLM consistently matches or surpasses leading Bayesian optimization and trust-region methods, while substantially outperforming global LLM-based sampling strategies.
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains challenging to decode them in a principled manner, because the nodes of a DAG can have many different topological orders. In this work, we propose a grammar-based approach to constructing a principled, compact and equivalent sequential representation of a DAG. Specifically, we view a graph as derivations over an unambiguous grammar, where the DAG corresponds to a unique sequence of production rules. Equivalently, the procedure to construct such a description can be viewed as a lossless compression of the data. Such a representation has many uses, including building a generative model for graph generation, learning a latent space for property prediction, and leveraging the sequence representational continuity for Bayesian Optimization over structured data. Code is available at https://github.com/shiningsunnyday/induction.
Retrieval-Augmented Generation (RAG) pipelines are central to applying large language models (LLMs) to proprietary or dynamic data. However, building effective RAG flows is complex, requiring careful selection among vector databases, embedding models, text splitters, retrievers, and synthesizing LLMs. The challenge deepens with the rise of agentic paradigms. Modules like verifiers, rewriters, and rerankers-each with intricate hyperparameter dependencies have to be carefully tuned. Balancing tradeoffs between latency, accuracy, and cost becomes increasingly difficult in performance-sensitive applications. We introduce syftr, a framework that performs efficient multi-objective search over a broad space of agentic and non-agentic RAG configurations. Using Bayesian Optimization, syftr discovers Pareto-optimal flows that jointly optimize task accuracy and cost. A novel early-stopping mechanism further improves efficiency by pruning clearly suboptimal candidates. Across multiple RAG benchmarks, syftr finds flows which are on average approximately 9 times cheaper while preserving most of the accuracy of the most accurate flows on the Pareto-frontier. Furthermore, syftr's ability to design and optimize allows integrating new modules, making it even easier and faster to realize high-performing generative AI pipelines.
Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent developments in steering protein generative models (e.g diffusion models, language models) offer a promising approach. However, by and large, past studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured by low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequence-fitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages compared to alternatives such as reinforcement learning with protein language models.
The rise of Large Audio Language Models (LAMs) brings both potential and risks, as their audio outputs may contain harmful or unethical content. However, current research lacks a systematic, quantitative evaluation of LAM safety especially against jailbreak attacks, which are challenging due to the temporal and semantic nature of speech. To bridge this gap, we introduce AJailBench, the first benchmark specifically designed to evaluate jailbreak vulnerabilities in LAMs. We begin by constructing AJailBench-Base, a dataset of 1,495 adversarial audio prompts spanning 10 policy-violating categories, converted from textual jailbreak attacks using realistic text to speech synthesis. Using this dataset, we evaluate several state-of-the-art LAMs and reveal that none exhibit consistent robustness across attacks. To further strengthen jailbreak testing and simulate more realistic attack conditions, we propose a method to generate dynamic adversarial variants. Our Audio Perturbation Toolkit (APT) applies targeted distortions across time, frequency, and amplitude domains. To preserve the original jailbreak intent, we enforce a semantic consistency constraint and employ Bayesian optimization to efficiently search for perturbations that are both subtle and highly effective. This results in AJailBench-APT, an extended dataset of optimized adversarial audio samples. Our findings demonstrate that even small, semantically preserved perturbations can significantly reduce the safety performance of leading LAMs, underscoring the need for more robust and semantically aware defense mechanisms.
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale to large datasets (which are common in modern applications), since it requires the solution of a linear system whose size scales quadratically with the number of samples in the dataset. We propose an approximate, distributed, accelerated sketch-and-project algorithm ($\texttt{ADASAP}$) for solving these linear systems, which improves scalability. We use the theory of determinantal point processes to show that the posterior mean induced by sketch-and-project rapidly converges to the true posterior mean. In particular, this yields the first efficient, condition number-free algorithm for estimating the posterior mean along the top spectral basis functions, showing that our approach is principled for GP inference. $\texttt{ADASAP}$ outperforms state-of-the-art solvers based on conjugate gradient and coordinate descent across several benchmark datasets and a large-scale Bayesian optimization task. Moreover, $\texttt{ADASAP}$ scales to a dataset with $> 3 \cdot 10^8$ samples, a feat which has not been accomplished in the literature.
The performance of an LLM depends heavily on the relevance of its training data to the downstream evaluation task. However, in practice, the data involved in an unseen evaluation task is often unknown (e.g., conversations between an LLM and a user are end-to-end encrypted). Hence, it is unclear what data are relevant for fine-tuning the LLM to maximize its performance on the specific unseen evaluation task. Instead, one can only deploy the LLM on the unseen task to gather multiple rounds of feedback on how well the model performs (e.g., user ratings). This novel setting offers a refreshing perspective towards optimizing training data mixtures via feedback from an unseen evaluation task, which prior data mixing and selection works do not consider. Our paper presents DUET, a novel global-to-local algorithm that interleaves influence function as a data selection method with Bayesian optimization to optimize data mixture via feedback from a specific unseen evaluation task. By analyzing DUET's cumulative regret, we theoretically show that DUET converges to the optimal training data mixture for an unseen task even without any data knowledge of the task. Finally, our experiments across a variety of language tasks demonstrate that DUET outperforms existing data selection and mixing methods in the unseen-task setting.
Bayesian optimization (BO) is a widely used algorithm for solving expensive black-box optimization problems. However, its performance decreases significantly on high-dimensional problems due to the inherent high-dimensionality of the acquisition function. In the proposed algorithm, we adaptively dropout the variables of the acquisition function along the iterations. By gradually reducing the dimension of the acquisition function, the proposed approach has less and less difficulty to optimize the acquisition function. Numerical experiments demonstrate that AdaDropout effectively tackle high-dimensional challenges and improve solution quality where standard Bayesian optimization methods often struggle. Moreover, it achieves superior results when compared with state-of-the-art high-dimensional Bayesian optimization approaches. This work provides a simple yet efficient solution for high-dimensional expensive optimization.
Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling methods and loss function weights for different PDEs, which reduces the efficiency of the solvers. In this paper, we pro- pose a general multi-stage framework, i.e. BO-SA-PINNs to alleviate this issue. In the first stage, Bayesian optimization (BO) is used to select hyperparameters for the training process, and based on the results of the pre-training, the network architecture, learning rate, sampling points distribution and loss function weights suitable for the PDEs are automatically determined. The proposed hyperparameters search space based on experimental results can enhance the efficiency of BO in identifying optimal hyperparameters. After selecting the appropriate hyperparameters, we incorporate a global self-adaptive (SA) mechanism the second stage. Using the pre-trained model and loss information in the second-stage training, the exponential moving average (EMA) method is employed to optimize the loss function weights, and residual-based adaptive refinement with distribution (RAR-D) is used to optimize the sampling points distribution. In the third stage, L-BFGS is used for stable training. In addition, we introduce a new activation function that enables BO-SA-PINNs to achieve higher accuracy. In numerical experiments, we conduct comparative and ablation experiments to verify the performance of the model on Helmholtz, Maxwell, Burgers and high-dimensional Poisson equations. The comparative experiment results show that our model can achieve higher accuracy and fewer iterations in test cases, and the ablation experiments demonstrate the positive impact of every improvement.
The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and evaluations might fail. The former challenge is addressed by Surrogate-Based Optimization (SBO) algorithms, in particular Bayesian Optimization (BO) using Gaussian Process (GP) models. An overview is provided of how BO can deal with challenges specific to architecture optimization, such as design variable hierarchy and multiple objectives: specific measures include ensemble infills and a hierarchical sampling algorithm. Evaluations might fail due to non-convergence of underlying solvers or infeasible geometry in certain areas of the design space. Such failed evaluations, also known as hidden constraints, pose a particular challenge to SBO/BO, as the surrogate model cannot be trained on empty results. This work investigates various strategies for satisfying hidden constraints in BO algorithms. Three high-level strategies are identified: rejection of failed points from the training set, replacing failed points based on viable (non-failed) points, and predicting the failure region. Through investigations on a set of test problems including a jet engine architecture optimization problem, it is shown that best performance is achieved with a mixed-discrete GP to predict the Probability of Viability (PoV), and by ensuring selected infill points satisfy some minimum PoV threshold. This strategy is demonstrated by solving a jet engine architecture problem that features at 50% failure rate and could not previously be solved by a BO algorithm. The developed BO algorithm and used test problems are available in the open-source Python library SBArchOpt.
This study focuses on mixed-variable black-box optimization (MV-BBO), addressing continuous, integer, and categorical variables. Many real-world MV-BBO problems involve dependencies among these different types of variables, requiring efficient methods to optimize them simultaneously. Recently, stochastic optimization methods leveraging the mechanism of the covariance matrix adaptation evolution strategy have shown promising results in mixed-integer or mixed-category optimization. However, such methods cannot handle the three types of variables simultaneously. In this study, we propose CatCMA with Margin (CatCMAwM), a stochastic optimization method for MV-BBO that jointly optimizes continuous, integer, and categorical variables. CatCMAwM is developed by incorporating a novel integer handling into CatCMA, a mixed-category black-box optimization method employing a joint distribution of multivariate Gaussian and categorical distributions. The proposed integer handling is carefully designed by reviewing existing integer handlings and following the design principles of CatCMA. Even when applied to mixed-integer problems, it stabilizes the marginal probability and improves the convergence performance of continuous variables. Numerical experiments show that CatCMAwM effectively handles the three types of variables, outperforming state-of-the-art Bayesian optimization methods and baselines that simply incorporate existing integer handlings into CatCMA.
Large Language Models (LLMs) can encode complex relationships in their latent spaces, yet harnessing them for optimization under uncertainty remains challenging. We address this gap with a novel architecture that reframes LLM finetuning as Gaussian process (GP) marginal likelihood optimization via deep kernel methods. We introduce LLM-based deep kernels, jointly optimized with GPs to preserve the benefits of both - LLMs to provide a rich and flexible input space for Bayesian optimization and - GPs to model this space with predictive uncertainty for more efficient sampling. Applied to Buchwald-Hartwig reaction optimization, our method nearly doubles the discovery rate of high-performing reactions compared to static LLM embeddings (from 24% to 43% coverage of the top 5% reactions in just 50 optimization iterations). We also observe a 14% improvement over domain-specific representations without requiring specialized features. Extensive empirical evaluation across 19 benchmarks - ranging from general chemistry to reaction and molecular property optimization - demonstrates our method's robustness, generality, and consistent improvements across: (1) tasks, (2) LLM architectures (encoder, decoder, encoder-decoder), (3) pretraining domains (chemistry-related or general-purpose) and (4) hyperparameter settings (tuned once on a single dataset). Finally, we explain these improvements: joint LLM-GP optimization through marginal likelihood implicitly performs contrastive learning, aligning representations to produce (1) better-structured embedding spaces, (2) improved uncertainty calibration, and (3) more efficient sampling - without requiring any external loss. This work provides both practical advances in sample-efficient optimization and insights into what makes effective Bayesian optimization.
Solving black-box optimization problems with Ising machines is increasingly common in materials science. However, their application to crystal structure prediction (CSP) is still ineffective due to symmetry agnostic encoding of atomic coordinates. We introduce CRYSIM, an algorithm that encodes the space group, the Wyckoff positions combination, and coordinates of independent atomic sites as separate variables. This encoding reduces the search space substantially by exploiting the symmetry in space groups. When CRYSIM is interfaced to Fixstars Amplify, a GPU-based Ising machine, its prediction performance was competitive with CALYPSO and Bayesian optimization for crystals containing more than 150 atoms in a unit cell. Although it is not realistic to interface CRYSIM to current small-scale quantum devices, it has the potential to become the standard CSP algorithm in the coming quantum age.