Expert-guided Bayesian optimization for sustainable protein formulation

Diversifying protein sources away from animal agriculture is critical for climate change mitigation and food security, but formulating sustainable protein sources that match or improve upon the properties of their animal-based counterparts remains an expensive trial-and-error process. We frame this challenge as high-dimensional black-box optimization with sparse approximate solutions and formalize Expert-Guided Bayesian Optimization (EGBO), in which an expert, e.g. a human or LLM, selects a low-dimensional subspace for BO and may adaptively expand it over time. We decompose EGBO's suboptimality into a selection gap and an optimization gap, and characterize the coverage–dimension tradeoff governing when expert guidance helps. To support in silico prototyping before costly real-world deployment, we introduce FormulateBench, a suite of 24 plant-based formulation tasks, on which LLM-guided EGBO outperforms all tested baselines. When deployed to optimize two plant-based dairy products, EGBO improves utility, as assessed by a trained human panel, by 29\% and 26\% in 10 iterations each. In a comparison with a professional human food scientist given the same time budget, EGBO achieved near-perfect utility of 0.992, vs. 0.850 for the food scientist.