Bayesian optimization (BO) has emerged as a potent tool for addressing intricate decision-making challenges, especially in public policy domains such as police districting. However, its broader application in public policymaking is hindered by the complexity of defining feasible regions and the high-dimensionality of decisions. This paper introduces the Hidden-Constrained Latent Space Bayesian Optimization (HC-LSBO), a novel BO method integrated with a latent decision model. This approach leverages a variational autoencoder to learn the distribution of feasible decisions, enabling a two-way mapping between the original decision space and a lower-dimensional latent space. By doing so, HC-LSBO captures the nuances of hidden constraints inherent in public policymaking, allowing for optimization in the latent space while evaluating objectives in the original space. We validate our method through numerical experiments on both synthetic and real data sets, with a specific focus on large-scale police districting problems in Atlanta, Georgia. Our results reveal that HC-LSBO offers notable improvements in performance and efficiency compared to the baselines.

翻译：贝叶斯优化（BO）已成为解决复杂决策挑战的有力工具，尤其在警务分区等公共政策领域。然而，其在公共政策制定中的广泛应用受到可行域定义复杂性与决策高维性的制约。本文提出含隐藏约束的潜在空间贝叶斯优化（HC-LSBO）——一种与潜在决策模型集成的新型BO方法。该方法利用变分自编码器学习可行决策的分布，实现原始决策空间与低维潜在空间之间的双向映射。通过这种方式，HC-LSBO捕捉公共政策制定中固有隐藏约束的细微特征，能够在潜在空间进行优化，同时在原始空间评估目标函数。我们通过合成数据集与真实数据集的数值实验验证该方法有效性，并特别聚焦于佐治亚州亚特兰大市的大规模警务分区问题。结果表明，与基线方法相比，HC-LSBO在性能与效率方面均取得显著提升。