# LLINBO: Trustworthy LLM-in-the-Loop Bayesian Optimization

arXiv: https://arxiv.org/abs/2505.14756 · HTML: https://mlsanity.com/paper/2505.14756/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations](https://mlsanity.com/paper/1908.01425/) (2019)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [πBO: Augmenting Acquisition Functions with User Beliefs for Bayesian Optimization](https://mlsanity.com/paper/2204.11051/) (2022)
- [On the generalization of language models from in-context learning and finetuning: a controlled study](https://mlsanity.com/paper/2505.00661/) (2025)
- [Towards Optimizing with Large Language Models](https://mlsanity.com/paper/2310.05204/) (2023)
- [Differentially Private Federated Bayesian Optimization with Distributed Exploration](https://mlsanity.com/paper/2110.14153/) (2021)
- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [Position: Leverage Foundational Models for Black-Box Optimization](https://mlsanity.com/paper/2405.03547/) (2024)
- [Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design](https://mlsanity.com/paper/2306.14348/) (2023)
- [Collaborative and Federated Black-box Optimization: A Bayesian Optimization Perspective](https://mlsanity.com/paper/2411.07523/) (2024)

## Built on by (most cited first, 14 of 14)

- [Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery](https://mlsanity.com/paper/2605.17976/) (2026)
- [LABO: LLM-Accelerated Bayesian Optimization through Broad Exploration and Selective Experimentation](https://mlsanity.com/paper/2605.22054/) (2026)
- [Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch](https://mlsanity.com/paper/2608.00316/) (2026)
- [Dynamic Priors in Bayesian Optimization for Hyperparameter Optimization](https://mlsanity.com/paper/2511.02570/) (2025)
- [SemanticOpt: Towards LLM-Based Semantic Black-Box Optimization](https://mlsanity.com/paper/2510.25404/) (2025)
- [Preference Learning from Physics-Based Feedback: Tuning Language Models to Design BCC/B2 Superalloys](https://mlsanity.com/paper/2511.12036/) (2025)
- [Elicitation Matters: How Prompts and Query Protocols Shape LLM Surrogates under Sparse Observations](https://mlsanity.com/paper/2605.04764/) (2026)
- [MALBO: Optimizing LLM-Based Multi-Agent Teams via Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2511.11788/) (2025)
- [MolLIBRA: Genetic Molecular Optimization with Multi-Fingerprint Surrogates and Text-Molecule Aligned Critic](https://mlsanity.com/paper/2602.07002/) (2026)
- [Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search](https://mlsanity.com/paper/2608.15669/) (2026)
- [LLMs as Acquisition Policies for Finite-Pool Materials Optimization: A Controlled Study](https://mlsanity.com/paper/2608.19790/) (2026)
- [Bayesian Optimization with Rich Auxiliary Information via LLMs](https://mlsanity.com/paper/2609.19437/) (2026)
- [Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search](https://mlsanity.com/paper/2609.34281/) (2026)
- [A Closer Look at Agentic BBO: Benchmarking LLM Agents for Black-Box Optimization](https://mlsanity.com/paper/2610.12183/) (2026)

## Abstract (arXiv)

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, relying solely on LLMs as optimization agents introduces risks due to their lack of explicit surrogate modeling and calibrated uncertainty, as well as their inherently opaque internal mechanisms. This structural opacity makes it difficult to characterize or control the exploration-exploitation trade-off, ultimately undermining theoretical tractability and reliability. To address this, we propose LLINBO: LLM-in-the-Loop BO, a hybrid framework for BO that combines LLMs with statistical surrogate experts (e.g., Gaussian Processes (GP)). The core philosophy is to leverage contextual reasoning strengths of LLMs for early exploration, while relying on principled statistical models to guide efficient exploitation. Specifically, we introduce three mechanisms that enable this collaboration and establish their theoretical guarantees. We end the paper with a real-life proof-of-concept in the context of 3D printing. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/LLM-in-the-Loop-BO.