# Adaptive Acquisition Selection for Bayesian Optimization with Large Language Models

arXiv: https://arxiv.org/abs/2602.07904 · HTML: https://mlsanity.com/paper/2602.07904/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Meta-Learning Acquisition Functions for Transfer Learning in Bayesian Optimization](https://mlsanity.com/paper/1904.02642/) (2019)
- [LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language](https://mlsanity.com/paper/2405.12856/) (2024)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Reinforced Few-Shot Acquisition Function Learning for Bayesian Optimization](https://mlsanity.com/paper/2106.04335/) (2021)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [An Entropy Search Portfolio for Bayesian Optimization](https://mlsanity.com/paper/1406.4625/) (2014)
- [No-PASt-BO: Normalized Portfolio Allocation Strategy for Bayesian Optimization](https://mlsanity.com/paper/1908.00361/) (2019)

## Built on by (most cited first, 9 of 9)

- [Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch](https://mlsanity.com/paper/2608.00316/) (2026)
- [Automated Kernel Discovery Towards Understanding High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2605.20249/) (2026)
- [Evidence-Gated LLM Priors for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2606.01730/) (2026)
- [Bayesian Optimization with Rich Auxiliary Information via LLMs](https://mlsanity.com/paper/2609.19437/) (2026)
- [Portfolio-Based Constrained Multi-Objective Bayesian Optimization for Materials Design](https://mlsanity.com/paper/2609.19550/) (2026)
- [Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search](https://mlsanity.com/paper/2609.34281/) (2026)
- [Agentic Resource Allocation for Batch Multi-Objective Bayesian Optimization in Autonomous Materials Discovery](https://mlsanity.com/paper/2610.04134/) (2026)
- [Agentic-MatriBO: Capability-Compiled Agentic Bayesian Optimization for Materials and Chemical Design](https://mlsanity.com/paper/2610.17832/) (2026)
- [JockeyBench: Evaluating LLM Agents on Horse-Racing Decision-Making](https://mlsanity.com/paper/2610.19589/) (2026)

## Abstract (arXiv)

Bayesian Optimization critically depends on the choice of acquisition function, but no single strategy is universally optimal; the best choice is non-stationary and problem-dependent. Existing adaptive portfolio methods often base their decisions on past function values while ignoring richer information like remaining budget or surrogate model characteristics. To address this, we introduce LMABO, a novel framework that casts a pre-trained Large Language Model (LLM) as a zero-shot, online strategist for the BO process. At each iteration, LMABO uses a structured state representation to prompt the LLM to select the most suitable acquisition function from a diverse portfolio. In an evaluation across 50 benchmark problems, LMABO demonstrates a significant performance improvement over strong static, adaptive portfolio, and other LLM-based baselines. We show that the LLM's behavior is a comprehensive strategy that adapts to real-time progress, proving its advantage stems from its ability to process and synthesize the complete optimization state into an effective, adaptive policy.