Robust Bayesian Optimization with Q-Exponential Surrogates

Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance. Here we present a systematic, compute-aware study of BO that evaluates surrogate models along two axes: optimization quality and computational frugality. Across eight benchmark functions and nine real-world datasets spanning materials science, mechanics, robotics, chemistry, and machine learning, we benchmark four surrogate models: Gaussian Processes, Random Forests, NGBoost, and Bayesian Adaptive Spline Surfaces. We show that Gaussian Process-based BO consistently incurs the highest time and memory overhead without delivering superior optimization or sample efficiency. In contrast, scalable alternatives achieve equal or better performance at a fraction of the computational cost. Motivated by these findings, we introduce a surrogate-recommendation framework that predicts the most suitable BO surrogate from inexpensive dataset characteristics. Together, these results establish FruBO as a reproducible, compute-aware baseline for Bayesian Optimization and provide practical guidance for surrogate selection under limited computational and experimental budgets.

Existing cumulative regret guarantees for Bayesian optimization (BO) do not necessarily characterize the quality of the algorithm's final output. This gap is critical under noisy evaluations, where the goal is to return a single high-quality recommendation. To address it, we introduce efficient exploration strategies that can be incorporated into any BO procedure by occasionally replacing the acquisition query with an exploration query. To validate this approach, we bound the Gaussian process posterior standard deviation over the search space via the fill distance of the queries, which measures the largest region left unexplored. We then use this result to derive upper bounds on the inference regret, i.e., the gap between the global optimum and the function value at the algorithm's returned point. Empirically, these exploration strategies improve the final recommendations of existing BO algorithms on synthetic benchmarks, hyperparameter optimization, and a control task.

Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian inference relies on the assumption that one's statistical model of the data-generating process is correctly specified. If this assumption is violated, Bayesian methods can lead to poor inference and estimates of information gain. Generalised Bayesian (or Gibbs) inference is a more robust probabilistic inference framework that replaces the likelihood in the Bayesian update by a suitable loss function. In this work, we present Generalised Bayesian Optimal Experimental Design (GBOED), an extension of generalised Bayesian inference to the experimental design setting which achieves robustness in both design and inference. Using a generalisation of Bayesian decision theory, we derive a new acquisition function, the Gibbs expected information gain. Our empirical results demonstrate that GBOED can enhance robustness to outliers and incorrect assumptions about the outcome noise distribution.