# Triangulation candidates for Bayesian optimization

arXiv: https://arxiv.org/abs/2112.07457 · HTML: https://mlsanity.com/paper/2112.07457/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 69 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 18 of 18)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [GLASSES: Relieving The Myopia Of Bayesian Optimisation](https://mlsanity.com/paper/1510.06299/) (2015)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Practical Transfer Learning for Bayesian Optimization](https://mlsanity.com/paper/1802.02219/) (2018)
- [Bayesian Optimization for Policy Search via Online-Offline Experimentation](https://mlsanity.com/paper/1904.01049/) (2019)
- [Adaptive Design of Experiments for Conservative Estimation of Excursion Sets](https://mlsanity.com/paper/1611.07256/) (2016)
- [Contour location via entropy reduction leveraging multiple information sources](https://mlsanity.com/paper/1805.07489/) (2018)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Distance-distributed design for Gaussian process surrogates](https://mlsanity.com/paper/1812.02794/) (2018)

## Built on by (most cited first, 11 of 11)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Improving LLM-based Global Optimization with Search Space Partitioning](https://mlsanity.com/paper/2505.21372/) (2025)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Voronoi Candidates for Bayesian Optimization](https://mlsanity.com/paper/2402.04922/) (2024)
- [Bayesian Optimization with Inexact Acquisition: Is Random Grid Search Sufficient?](https://mlsanity.com/paper/2506.11831/) (2025)
- [Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators](https://mlsanity.com/paper/2410.01196/) (2024)
- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)
- [Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions](https://mlsanity.com/paper/2411.16206/) (2024)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)

## Abstract (arXiv)

Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suited for hybrid schemes, on benchmark synthetic and real simulation experiments.