# Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization

arXiv: https://arxiv.org/abs/2210.01628 · HTML: https://mlsanity.com/paper/2210.01628/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 25 of 25)

- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [NAS-Bench-1Shot1: Benchmarking and Dissecting One-shot Neural Architecture Search](https://mlsanity.com/paper/2001.10422/) (2020)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [TransNAS-Bench-101: Improving Transferability and Generalizability of Cross-Task Neural Architecture Search](https://mlsanity.com/paper/2105.11871/) (2021)
- [High Dimensional Bayesian Optimization Using Dropout](https://mlsanity.com/paper/1802.05400/) (2018)
- [On the choice of the low-dimensional domain for global optimization via random embeddings](https://mlsanity.com/paper/1704.05318/) (2017)
- [Decentralized High-Dimensional Bayesian Optimization with Factor Graphs](https://mlsanity.com/paper/1711.07033/) (2017)
- [High-Dimensional Bayesian Optimization via Tree-Structured Additive Models](https://mlsanity.com/paper/2012.13088/) (2020)
- [A warped kernel improving robustness in Bayesian optimization via random embeddings](https://mlsanity.com/paper/1411.3685/) (2014)
- [Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection](https://mlsanity.com/paper/2109.09264/) (2021)
- [Bayesian Optimization using Pseudo-Points](https://mlsanity.com/paper/1910.05484/) (2019)

## Built on by (most cited first, 30 of 37)

- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [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)
- [Understanding High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2502.09198/) (2025)
- [Offline Multi-Objective Optimization](https://mlsanity.com/paper/2406.03722/) (2024)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models](https://mlsanity.com/paper/2405.08674/) (2024)
- [Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2305.19838/) (2023)
- [Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation](https://mlsanity.com/paper/2307.13371/) (2023)
- [Monte Carlo Tree Search based Space Transfer for Black-box Optimization](https://mlsanity.com/paper/2412.07186/) (2024)
- [High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy](https://mlsanity.com/paper/2402.03104/) (2024)
- [High-dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2310.03515/) (2023)
- [Joint Composite Latent Space Bayesian Optimization](https://mlsanity.com/paper/2311.02213/) (2023)
- [BBOPlace-Bench: Benchmarking Black-Box Optimization for Chip Placement](https://mlsanity.com/paper/2510.23472/) (2025)
- [Racing Control Variable Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2309.07934/) (2023)
- [Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems](https://mlsanity.com/paper/2412.20350/) (2024)
- [High Dimensional Bayesian Optimization using Lasso Variable Selection](https://mlsanity.com/paper/2504.01743/) (2025)
- [Bayesian Optimisation Against Climate Change: Applications and Benchmarks](https://mlsanity.com/paper/2306.04343/) (2023)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [No-Regret Learning of Nash Equilibrium for Black-Box Games via Gaussian Processes](https://mlsanity.com/paper/2405.08318/) (2024)
- [Expected Coordinate Improvement for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2404.11917/) (2024)
- [Navigating in High-Dimensional Search Space: A Hierarchical Bayesian Optimization Approach](https://mlsanity.com/paper/2410.23148/) (2024)
- [Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2504.06111/) (2025)
- [Enhancing Trust-Region Bayesian Optimization via Newton Methods](https://mlsanity.com/paper/2508.18423/) (2025)
- [Rethinking Trust Region Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2604.22967/) (2026)
- [NeuroPareto: Calibrated Acquisition for Costly Many-Goal Search in Vast Parameter Spaces](https://mlsanity.com/paper/2602.03901/) (2026)
- [Automated Kernel Discovery Towards Understanding High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2605.20249/) (2026)
- [Improve Value Estimation of Q Function and Reshape Reward with Monte Carlo Tree Search](https://mlsanity.com/paper/2410.11642/) (2024)
- [An Adaptive Dropout Approach for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2504.11353/) (2025)
- [BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/2508.02332/) (2025)

## Abstract (arXiv)

Bayesian optimization (BO) is a class of popular methods for expensive black-box optimization, and has been widely applied to many scenarios. However, BO suffers from the curse of dimensionality, and scaling it to high-dimensional problems is still a challenge. In this paper, we propose a variable selection method MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select and optimize a subset of variables. That is, MCTS-VS constructs a low-dimensional subspace via MCTS and optimizes in the subspace with any BO algorithm. We give a theoretical analysis of the general variable selection method to reveal how it can work. Experiments on high-dimensional synthetic functions and real-world problems (i.e., NAS-bench problems and MuJoCo locomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can achieve state-of-the-art performance.