{"ID":2859586,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.06439","arxiv_id":"2510.06439","title":"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. Compared with a conventional one-dimensional Monte Carlo-based optimization scheme, the proposed approach requires 40 times fewer data points, resulting in up to a 40-fold reduction in computational cost. We demonstrate the effectiveness of the proposed method through two numerical examples in computational engineering.","short_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 uncertaint...","url_abs":"https://arxiv.org/abs/2510.06439","url_pdf":"https://arxiv.org/pdf/2510.06439v1","authors":"[\"Akash Yadav\",\"Ruda Zhang\"]","published":"2025-10-07T20:19:51Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\",\"math.OC\",\"stat.ML\"]","methods":"[]","has_code":false}