SO-BO-scale: Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models

A Bayesian optimization framework for efficiently optimizing a scale parameter in stochastic models.

Optimization under uncertainty is challenging due to noisy function evaluations.

This repository provides an approach that leverages a statistical surrogate for the objective function, enabling analytical evaluation of expectations. We also derive a closed-form solution for optimizing a random acquisition function, significantly reducing the computational cost per iteration.

The code demonstrates the effectiveness of the proposed approach for optimizing the scale parameter of SS-PPCA across static and dynamic problems, and compares against GP-based BO and SOTA noisy-BO baselines.

Repository Layout

Ex1/   — Linear static problem
Ex2/   — Linear dynamics problem
Ex3/   — Non power-law problem

Each example folder contains:

• BO/ — Proposed Bayesian optimization (MATLAB)
• GP/ — GP-based BO baseline (Python + MATLAB plotting)
• 1D/ — 1D Monte Carlo baseline (MATLAB)
• SOTA_BO/ — SOTA noisy-BO baselines: qLogNEI and qNEI (Python + MATLAB plotting)
• Model/ — Precomputed data and model-specific files

Additionally:

• Robustness/ — Multi-seed robustness study across all methods and examples

Requirements

MATLAB

• R2023b or later
• Statistics and Machine Learning Toolbox
• Optimization Toolbox

Python

• numpy
• scipy
• matplotlib
• torch
• gpytorch
• botorch

The code was developed for a Linux environment where python and matlab are both available on PATH.

Quick Start

Clone the repository:

git clone https://github.com/UQUH/SO-BO-scale.git
cd SO-BO-scale

Run the full robustness study

bash Robustness/run_study.sh --example all

Results are written to Robustness/Ex*/ and include per-seed .mat files, aggregated summary CSVs, and convergence plots.

Dry run on one seed

bash Robustness/run_study.sh --example Ex1 --max-seeds 1 --rebuild-truth

Reproducing Individual Example Runs

Proposed BO method

Open MATLAB, set the example BO/ folder as the working directory, and run the corresponding script (e.g., Ex1_BO.m).

GP baseline

# Example 1
python Ex1/GP/bo_ex1.py
matlab -batch "cd('Ex1/GP'); plot_gp_bo_ex1"

# Example 2
python Ex2/GP/bo_ex2.py
matlab -batch "cd('Ex2/GP'); plot_gp_bo_ex2"

# Example 3
python Ex3/GP/bo_ex3.py
matlab -batch "cd('Ex3/GP'); plot_gp_bo_ex3"

SOTA noisy-BO baselines

qLogNEI and qNEI wrappers are provided for 1, 5, and 10 MC samples per objective evaluation.

Example: qLogNEI with 10 MC samples:

python Ex1/SOTA_BO/bo_ex1_sota_mc10.py
matlab -batch "cd('Ex1/SOTA_BO'); plot_sota_bo_ex1_mc10"

For qNEI, use the corresponding bo_ex*_qnei_mc*.py and plot_sota_bo_ex*_qnei_mc*.m files.

Citation

If you find the SO-BO-scale helpful, please cite the following paper:

@misc{yadav2025SO-BO-scale,
      title={Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models},
      author={Akash Yadav and Ruda Zhang},
      year={2025},
      eprint={2510.06439},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2510.06439},
}

The Team

The SO-BO-scale method was developed by the Uncertainty Quantification Lab at the University of Houston.

Primary contributors:

• Akash Yadav
• Ruda Zhang