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

• URL: http://arxiv.org/abs/2510.06439v1
• Date: Tue, 07 Oct 2025 20:19:51 GMT
• Title: Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models
• Authors: Akash Yadav, Ruda Zhang,
• Abstract summary: We present a novel framework tailored for hyperparameter tuning under uncertainty.<n>The proposed method employs a statistical surrogate for the underlying random variable, enabling the evaluation of the expectation operator.<n>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.
• Score: 3.7527745397166754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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