# Constrained Bayesian Optimisation with Multiple Information Sources

arXiv: https://arxiv.org/abs/2607.00865 · HTML: https://mlsanity.com/paper/2607.00865/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 19 of 19)

- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [A General Framework for Constrained Bayesian Optimization using Information-based Search](https://mlsanity.com/paper/1511.09422/) (2015)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [MUMBO: MUlti-task Max-value Bayesian Optimization](https://mlsanity.com/paper/2006.12093/) (2020)
- [Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization](https://mlsanity.com/paper/1901.08275/) (2019)
- [Constrained Bayesian Optimization with Max-Value Entropy Search](https://mlsanity.com/paper/1910.07003/) (2019)
- [Multi-Fidelity Bayesian Optimization with Unreliable Information Sources](https://mlsanity.com/paper/2210.13937/) (2022)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)
- [Feasibility-Driven Trust Region Bayesian Optimization](https://mlsanity.com/paper/2506.14619/) (2025)
- [Constrained multi-fidelity Bayesian optimization with automatic stop condition](https://mlsanity.com/paper/2503.01126/) (2025)

## Abstract (arXiv)

Bayesian Optimisation (BO) under unknown constraints is particularly challenging when feasible regions are small. In such settings, existing methods that typically rely solely on evaluations of the true objective and constraints struggle to efficiently explore the design space. However, many real-world applications offer auxiliary data sources (e.g. surrogate models or simplified simulations) that can support early exploration. Despite this potential, their integration into constrained BO remains largely unexplored. We propose a general multi-source framework that extends constrained Max-value Entropy Search, capturing inter-source correlation while balancing evaluation cost and information gain. Experiments on both synthetic and physics-based benchmarks show that our method efficiently identifies feasible and optimal solutions, even when auxiliary data are only weakly correlated. The proposed approach consistently outperforms existing methods, particularly in early-stage exploration.