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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Yadav, Akash, Zhang, Ruda
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912634479050752
author Yadav, Akash
Zhang, Ruda
author_facet Yadav, Akash
Zhang, Ruda
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06439
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models
Yadav, Akash
Zhang, Ruda
Machine Learning
Computational Engineering, Finance, and Science
Optimization and Control
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.
title Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models
topic Machine Learning
Computational Engineering, Finance, and Science
Optimization and Control
url https://arxiv.org/abs/2510.06439