# Evidence-Gated LLM Priors for Multi-Objective Bayesian Optimization

arXiv: https://arxiv.org/abs/2606.01730 · HTML: https://mlsanity.com/paper/2606.01730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 1 Jun 2026.

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

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [InstructZero: Efficient Instruction Optimization for Black-Box Large Language Models](https://mlsanity.com/paper/2306.03082/) (2023)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs](https://mlsanity.com/paper/2509.17998/) (2025)
- [Bayesian Optimization of Antibodies Informed by a Generative Model of Evolving Sequences](https://mlsanity.com/paper/2412.07763/) (2024)
- [Adaptive Feature-based Low-Rank Compression of Large Language Models via Bayesian Optimization](https://mlsanity.com/paper/2405.10616/) (2024)
- [Hyperband-based Bayesian Optimization for Black-box Prompt Selection](https://mlsanity.com/paper/2412.07820/) (2024)
- [Data Mixture Optimization: A Multi-fidelity Multi-scale Bayesian Framework](https://mlsanity.com/paper/2503.21023/) (2025)
- [Adaptive Acquisition Selection for Bayesian Optimization with Large Language Models](https://mlsanity.com/paper/2602.07904/) (2026)
- [Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery](https://mlsanity.com/paper/2605.17976/) (2026)
- [Model Fusion through Bayesian Optimization in Language Model Fine-Tuning](https://mlsanity.com/paper/2411.06710/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used as heuristic advisors for black-box optimization, yet their suggestions and self-reported confidence are not necessarily calibrated to downstream objective values. This issue becomes more pronounced in multi-objective Bayesian optimization, where different objectives may require different expert knowledge and where an LLM expert can be useful for one objective but misleading for another. We study how to use LLM-generated expert priors in discrete multi-objective Bayesian optimization without blindly trusting them. We propose an objective-wise reputation-market mechanism that treats each expert-objective pair as a falsifiable prior source. Expert weights are updated online from observed objective feedback, discounted over time, and gated by market-level trust. We then introduce a decoupled counterfactual gate that can use the LLM prior without confidence, use it with confidence, or abstain from the LLM prior entirely. Across controlled synthetic stress tests and three molecule optimization benchmarks with qwenflash-generated expert priors, we find that dynamic objective-wise calibration improves robustness over fixed LLM priors. However, raw LLM confidence is not reliably beneficial: on ESOL, confidence is positively correlated with prediction error; on FreeSolv, confidence can help; and on Lipophilicity, ignoring confidence remains strongest. Our fixed three-arm counterfactual gate improves over the first counterfactual variant on ESOL and FreeSolv, while an attempted margin portfolio exposes a useful negative result: margin selection should be acquisition-aware rather than based only on one-step prior error.