Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models

Abstract

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertainty, with a focus on optimizing a scale- or precision-type parameter in stochastic models. The proposed method employs a statistical surrogate for the underlying random variable, enabling analytical evaluation of the expectation operator. Moreover, we derive a closed-form expression for the optimizer of the random acquisition function, which significantly reduces computational cost per iteration. Numerical experiments demonstrate substantial gains in optimization efficiency: about 40-fold reduction in data usage relative to a Monte Carlo-based one-dimensional optimization scheme, and an order of magnitude improvement relative to a Gaussian process-based Bayesian optimization baseline.

arXiv comment25 pages, 23 figures, 3 tables. Code: https://github.com/UQUH/SO-BO-scale