Bayesian Optimization for Mixed-Variable Problems in the Natural Sciences
This work provides a practical BO framework for mixed-variable optimization problems in the natural sciences, particularly useful in autonomous laboratory settings with noise and limited data, but it is incremental as it builds on existing PR methods.
The paper tackled the problem of Bayesian optimization (BO) becoming less effective in mixed or high-cardinality discrete spaces by generalizing the probabilistic reparameterization (PR) approach to handle non-equidistant discrete variables, enabling gradient-based optimization with Gaussian process surrogates and demonstrating robustness in benchmarks on synthetic and experimental objectives.
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.