# Unbounded Bayesian Optimization via Regularization

arXiv: https://arxiv.org/abs/1508.03666 · HTML: https://mlsanity.com/paper/1508.03666/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2015.

## Built on by (most cited first, 13 of 13)

- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [πBO: Augmenting Acquisition Functions with User Beliefs for Bayesian Optimization](https://mlsanity.com/paper/2204.11051/) (2022)
- [Transfer Learning for Bayesian Optimization: A Survey](https://mlsanity.com/paper/2302.05927/) (2023)
- [Sequential Large Language Model-Based Hyper-parameter Optimization](https://mlsanity.com/paper/2410.20302/) (2024)
- [Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization](https://mlsanity.com/paper/2303.05694/) (2023)
- [Sparse Bayesian Optimization](https://mlsanity.com/paper/2203.01900/) (2022)
- [High-dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2310.03515/) (2023)
- [Predicting the utility of search spaces for black-box optimization: a simple, budget-aware approach](https://mlsanity.com/paper/2112.08250/) (2021)
- [Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2504.06111/) (2025)
- [FastBO: Fast HPO and NAS with Adaptive Fidelity Identification](https://mlsanity.com/paper/2409.00584/) (2024)
- [Bifidelity Karhunen-Lo`eve Expansion Surrogate with Active Learning for Random Fields](https://mlsanity.com/paper/2511.03756/) (2025)
- [An Optimised Greedy-Weighted Ensemble Framework for Financial Loan Default Prediction](https://mlsanity.com/paper/2603.18927/) (2026)
- [Hierarchical Prompt-Domain Control and Learning for Resource-Constrained Agentic Language Models](https://mlsanity.com/paper/2605.27703/) (2026)

## Abstract (arXiv)

Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to contain the optimizer. However, when little is known about the probed objective function, it can be difficult to prescribe such bounds. In this work we modify the standard Bayesian optimization framework in a principled way to allow automatic resizing of the search space. We introduce two alternative methods and compare them on two common synthetic benchmarking test functions as well as the tasks of tuning the stochastic gradient descent optimizer of a multi-layered perceptron and a convolutional neural network on MNIST.