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

arXiv: https://arxiv.org/abs/2510.06439 · HTML: https://mlsanity.com/paper/2510.06439/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Epsilon-Greedy Thompson Sampling to Bayesian Optimization](https://mlsanity.com/paper/2403.00540/) (2024)
- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Optimizing Posterior Samples for Bayesian Optimization via Rootfinding](https://mlsanity.com/paper/2410.22322/) (2024)
- [Automated design of nonreciprocal thermal emitters via Bayesian optimization](https://mlsanity.com/paper/2409.09192/) (2024)
- [Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization](https://mlsanity.com/paper/2410.23482/) (2024)
- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
- [Demand, Supply, and Performance of Street-Hail Taxi](https://mlsanity.com/paper/1909.12861/) (2019)
- [Stochastic Subspace via Probabilistic Principal Component Analysis for Characterizing Model Error](https://mlsanity.com/paper/2504.19963/) (2025)

## Built on by (most cited first, 1 of 1)

- [Calibrating Scientific Foundation Models with Inference-Time Stochastic Attention](https://mlsanity.com/paper/2604.19530/) (2026)

## Abstract (arXiv)

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.