# A warped kernel improving robustness in Bayesian optimization via random embeddings

arXiv: https://arxiv.org/abs/1411.3685 · HTML: https://mlsanity.com/paper/1411.3685/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2014.

## Built on by (most cited first, 17 of 17)

- [Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces](https://mlsanity.com/paper/2102.07188/) (2021)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization](https://mlsanity.com/paper/2210.01628/) (2022)
- [Bounce: Reliable High-Dimensional Bayesian Optimization for Combinatorial and Mixed Spaces](https://mlsanity.com/paper/2307.00618/) (2023)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2305.19838/) (2023)
- [Global optimization using random embeddings](https://mlsanity.com/paper/2107.12102/) (2021)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [Learning Representation for Bayesian Optimization with Collision-free Regularization](https://mlsanity.com/paper/2203.08656/) (2022)
- [Expected Coordinate Improvement for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2404.11917/) (2024)
- [A model aggregation approach for high-dimensional large-scale optimization](https://mlsanity.com/paper/2205.07525/) (2022)
- [Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings](https://mlsanity.com/paper/2211.00947/) (2022)
- [High dimensional Bayesian Optimization via Condensing-Expansion Projection](https://mlsanity.com/paper/2408.04860/) (2024)
- [Scaling Bayesian Optimization With Game Theory](https://mlsanity.com/paper/2110.03790/) (2021)
- [Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization](https://mlsanity.com/paper/2501.14118/) (2025)
- [An Adaptive Dropout Approach for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2504.11353/) (2025)
- [Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization](https://mlsanity.com/paper/2510.15435/) (2025)

## Abstract (arXiv)

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.