# Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search

arXiv: https://arxiv.org/abs/2609.34281 · HTML: https://mlsanity.com/paper/2609.34281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 42 of its 50 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 30 of 42)

- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Benchmarking Model-Based Reinforcement Learning](https://mlsanity.com/paper/1907.02057/) (2019)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [Large Language Model Agent for Hyper-Parameter Optimization](https://mlsanity.com/paper/2402.01881/) (2024)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [High Dimensional Bayesian Optimization Using Dropout](https://mlsanity.com/paper/1802.05400/) (2018)
- [Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization](https://mlsanity.com/paper/2210.01628/) (2022)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [Standard Gaussian Process is All You Need for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2402.02746/) (2024)
- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [High-Dimensional Bayesian Optimization via Tree-Structured Additive Models](https://mlsanity.com/paper/2012.13088/) (2020)
- [Position: Leverage Foundational Models for Black-Box Optimization](https://mlsanity.com/paper/2405.03547/) (2024)
- [Understanding High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2502.09198/) (2025)
- [Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs](https://mlsanity.com/paper/2509.17998/) (2025)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [Language-Based Bayesian Optimization Research Assistant (BORA)](https://mlsanity.com/paper/2501.16224/) (2025)
- [Can LLMs Beat Classical Hyperparameter Optimization Algorithms? A Study on autoresearch](https://mlsanity.com/paper/2603.24647/) (2026)
- [LLINBO: Trustworthy LLM-in-the-Loop Bayesian Optimization](https://mlsanity.com/paper/2505.14756/) (2025)

## Abstract (arXiv)

High-dimensional Bayesian optimization (HDBO) seeks sample-efficient optimization when the number of variables is large relative to the evaluation budget. Recent LLM-based and agentic BO methods incorporate task knowledge and adapt search decisions during a run, but have primarily been evaluated on low- and moderate-dimensional problems. We ask whether this paradigm can transfer to the higher-dimensional regime. Our experiments show that these methods do not remain reliable in the high-dimensional regime, where the challenge is not only where to evaluate, but also which modeling assumption and search geometry to use when the objective's useful structure is unknown. We therefore introduce HERA, a Hypothesis- and Evidence-guided Research Agent that uses task context, optimization feedback, and structural diagnostics to revise search hypotheses, select and configure HDBO strategies, and determine their execution length. PRISM, its numerical optimization engine, generates and evaluates candidates sequentially within each search block, updating numerical models after each observation. HERA remains competitive with strong numerical HDBO baselines and outperforms the evaluated LLM-based and agentic methods on four metadata-free synthetic functions. Across eight real-world tasks, HERA achieves the best mean final objective among all evaluated systems on most benchmarks. Further analyses show that structural diagnostics change strategy use, metadata effects vary across tasks, and adaptive search blocks reduce inference cost.