# Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling

arXiv: https://arxiv.org/abs/2603.24567 · HTML: https://mlsanity.com/paper/2603.24567/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Understanding High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2502.09198/) (2025)
- [Feasibility-Driven Trust Region Bayesian Optimization](https://mlsanity.com/paper/2506.14619/) (2025)
- [Bayesian Optimization for CVaR-based portfolio optimization](https://mlsanity.com/paper/2503.17737/) (2025)

## Abstract (arXiv)

Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that combines a penalty formulation, a surrogate model, and a trust region strategy. The constrained problem is converted to an unconstrained form by penalizing constraint violations, which provides a unified modeling framework. A trust region restricts the search to a local region around the current best solution, which improves stability and efficiency in high dimensions. Within this region, we use the Expected Improvement acquisition function to select evaluation points by balancing improvement and uncertainty. The proposed Trust Region method integrates penalty-based constraint handling with local surrogate modeling. This combination enables efficient exploration of feasible regions while maintaining sample efficiency. We compare the proposed method with state-of-the-art methods on synthetic and real-world high-dimensional constrained optimization problems. The results show that the method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance across different settings.