# Bayesian Optimization for Mixed-Variable Problems in the Natural Sciences

arXiv: https://arxiv.org/abs/2604.07416 · HTML: https://mlsanity.com/paper/2604.07416/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces](https://mlsanity.com/paper/2102.07188/) (2021)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization](https://mlsanity.com/paper/2210.10199/) (2022)
- [Framework and Benchmarks for Combinatorial and Mixed-variable Bayesian Optimization](https://mlsanity.com/paper/2306.09803/) (2023)
- [BARK: A Fully Bayesian Tree Kernel for Black-box Optimization](https://mlsanity.com/paper/2503.05574/) (2025)

## Abstract (arXiv)

Optimizing expensive black-box objectives over mixed search spaces is a common challenge across the natural sciences. Bayesian optimization (BO) offers sample-efficient strategies through probabilistic surrogate models and acquisition functions. However, its effectiveness diminishes in mixed or high-cardinality discrete spaces, where gradients are unavailable and optimizing the acquisition function becomes computationally demanding. In this work, we generalize the probabilistic reparameterization (PR) approach of Daulton et al. to handle non-equidistant discrete variables, enabling gradient-based optimization in fully mixed-variable settings with Gaussian process (GP) surrogates. With real-world scientific optimization tasks in mind, we conduct systematic benchmarks on synthetic and experimental objectives to obtain an optimized kernel formulations and demonstrate the robustness of our generalized PR method. We additionally show that, when combined with a modified BO workflow, our approach can efficiently optimize highly discontinuous and discretized objective landscapes. This work establishes a practical BO framework for addressing fully mixed optimization problems in the natural sciences, and is particularly well suited to autonomous laboratory settings where noise, discretization, and limited data are inherent.