# High Dimensional Bayesian Optimization via Supervised Dimension Reduction

arXiv: https://arxiv.org/abs/1907.08953 · HTML: https://mlsanity.com/paper/1907.08953/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2019.

## Built on by (most cited first, 21 of 21)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Global optimization using random embeddings](https://mlsanity.com/paper/2107.12102/) (2021)
- [Joint Composite Latent Space Bayesian Optimization](https://mlsanity.com/paper/2311.02213/) (2023)
- [Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems](https://mlsanity.com/paper/2412.20350/) (2024)
- [High dimensional Bayesian Optimization Algorithm for Complex System in Time Series](https://mlsanity.com/paper/2108.02289/) (2021)
- [Expected Coordinate Improvement for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2404.11917/) (2024)
- [High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspaces](https://mlsanity.com/paper/2412.16554/) (2024)
- [Enhancing Trust-Region Bayesian Optimization via Newton Methods](https://mlsanity.com/paper/2508.18423/) (2025)
- [BO4Mob: Bayesian Optimization Benchmarks for High-Dimensional Urban Mobility Problem](https://mlsanity.com/paper/2510.18824/) (2025)
- [High-dimensional Bayesian Optimization Algorithm with Recurrent Neural Network for Disease Control Models in Time Series](https://mlsanity.com/paper/2201.00147/) (2022)
- [Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings](https://mlsanity.com/paper/2211.00947/) (2022)
- [An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2403.05425/) (2024)
- [Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space](https://mlsanity.com/paper/2407.11917/) (2024)
- [CobBO: Coordinate Backoff Bayesian Optimization with Two-Stage Kernels](https://mlsanity.com/paper/2101.05147/) (2021)
- [Simulating, Fast and Slow: Learning Policies for Black-Box Optimization](https://mlsanity.com/paper/2406.04261/) (2024)
- [Swine Diet Design using Multi-objective Regionalized Bayesian Optimization](https://mlsanity.com/paper/2409.12919/) (2024)
- [An Adaptive Dropout Approach for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2504.11353/) (2025)
- [Towards safe control parameter tuning in distributed multi-agent systems](https://mlsanity.com/paper/2508.13608/) (2025)
- [Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension](https://mlsanity.com/paper/2605.23473/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding structure for objective functions. This paper directly introduces a supervised dimension reduction method, Sliced Inverse Regression (SIR), to high dimensional Bayesian optimization, which could effectively learn the intrinsic sub-structure of objective function during the optimization. Furthermore, a kernel trick is developed to reduce computational complexity and learn nonlinear subset of the unknowing function when applying SIR to extremely high dimensional BO. We present several computational benefits and derive theoretical regret bounds of our algorithm. Extensive experiments on synthetic examples and two real applications demonstrate the superiority of our algorithms for high dimensional Bayesian optimization.