# Bayesian Optimization with Unknown Search Space

arXiv: https://arxiv.org/abs/1910.13092 · HTML: https://mlsanity.com/paper/1910.13092/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Automatic Termination for Hyperparameter Optimization](https://mlsanity.com/paper/2104.08166/) (2021)
- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [RcTorch: a PyTorch Reservoir Computing Package with Automated Hyper-Parameter Optimization](https://mlsanity.com/paper/2207.05870/) (2022)
- [Hyperparameter Optimization with Neural Network Pruning](https://mlsanity.com/paper/2205.08695/) (2022)
- [Advances in Medical Image Segmentation: A Comprehensive Survey with a Focus on Lumbar Spine Applications](https://mlsanity.com/paper/2510.03318/) (2025)

## Abstract (arXiv)

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.