[论文解读] Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling

Raju Chowdhury, Tanmay Sen+2 more|arXiv (Cornell University)|Mar 25, 2026

Advanced Multi-Objective Optimization Algorithms被引用 0

一句话总结

论文提出了TR-MEI，一种基于信任域的贝叶斯优化方法，使用大M惩罚来处理约束，在高维有约束优化中实现更高效的可行性和样本效率，与SCBO和FuRBO相比表现更好。

ABSTRACT

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.

研究动机与目标

• 解决高维黑箱有约束优化中评估代价高的挑战。
• 将大M惩罚的约束处理整合到贝叶斯优化框架中。
• 利用局部信任域在高维情形下提升稳定性与效率。
• 在惩罚后的目标中使用EI为基础的采集函数，平衡探索与利用。

提出的方法

• 通过对约束违规使用大M惩罚，将带约束的问题转化为无约束问题。
• 对目标和每个约束分别使用独立的高斯过程进行建模。
• 使用惩罚后目标的预测分布来定义惩罚性EI（M-EI）。
• 将优化限制在以当前最优解为中心的超矩形信任区域内。
• 基于进展进行反复更新代理模型与信任区域大小。

Figure 1: Ackley

实验结果

研究问题

• RQ1 TR-MEI是否在比现有高维有约束BO方法更少的评估次数下获得更高质量的可行解？
• RQ2 将大M惩罚与信任域结合是否能在高维有约束情境中提高稳定性与可扩展性？
• RQ3 在合成有约束基准测试中，TR-MEI在可行性与目标值方面与SCBO与FuRBO相比如何？
• RQ4 从不可行初始点出发时，基于惩罚的无约束形式是否仍然有效？

主要发现

• TR-MEI在基准问题上以更少的函数评估找到高质量的可行解。
• 在Ackley、Levy和Rastrigin（20D）上，TR-MEI比FuRBO和SCBO更快收敛到可行的最优解。
• TR-MEI在不同问题设置下表现出鲁棒性和稳定性。
• 由于惩罚机制引导可行性，方法允许从不可行点出发。
• 与SCBO和FuRBO相比，TR-MEI提供简单、解析可控的EI，而无需依赖汤普森采样。

Figure 2: Levy