# Can Bayesian Optimization Efficiently Find a Strong Single Expert in Neural Thickets?

arXiv: https://arxiv.org/abs/2608.10867 · HTML: https://mlsanity.com/paper/2608.10867/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 17 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning](https://mlsanity.com/paper/2509.24372/) (2025)
- [Evolution Strategies at the Hyperscale](https://mlsanity.com/paper/2511.16652/) (2025)
- [Learning to Reason in 13 Parameters](https://mlsanity.com/paper/2602.04118/) (2026)
- [MATH-Beyond: A Benchmark for RL to Expand Beyond the Base Model](https://mlsanity.com/paper/2510.11653/) (2025)

## Abstract (arXiv)

Gradient-free post-training has emerged as a compelling alternative to gradient-based optimization for large language models (LLMs), but existing approaches remain costly. We ask whether structured search can identify a strong single expert under a modest evaluation budget. Motivated by evidence that useful weight updates lie in low-dimensional subspaces, we apply Bayesian optimization within a random linear embedding of weight space. Our method requires no backpropagation and uses a Gaussian process surrogate to guide candidate evaluations efficiently. Across several reasoning benchmarks with Qwen2.5-Instruct models from 0.5B to 3B parameters, Bayesian optimization using five times less candidate evaluations matches or exceeds RandOpt. These results show that surrogate-guided search can substantially reduce the evaluation cost of gradient-free post-training while producing stronger deployable single experts.