Black-box optimization (BBO) has become increasingly relevant for tackling complex decision-making problems, 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 a novel BBO framework, termed as the Conditional And Generative Black-box Optimization (CageBO). This approach leverages a conditional variational autoencoder to learn the distribution of feasible decisions, enabling a two-way mapping between the original decision space and a simplified, constraint-free latent space. The CageBO efficiently handles the implicit constraints often found in public policy applications, allowing for optimization in the latent space while evaluating objectives in the original space. We validate our method through a case study on large-scale police districting problems in Atlanta, Georgia. Our results reveal that our CageBO offers notable improvements in performance and efficiency compared to the baselines.

翻译：黑箱优化（BBO）在处理复杂决策问题中日益重要，尤其在警察片区划分等公共政策领域。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和决策高维度的制约。本文提出一种新颖的黑箱优化框架，称为条件生成黑箱优化（CageBO）。该方法利用条件变分自编码器学习可行决策的分布，实现原始决策空间与简化无约束潜空间之间的双向映射。CageBO高效处理公共政策应用中常见的隐式约束，可在潜空间进行优化，同时在原始空间评估目标函数。我们通过佐治亚州亚特兰大市大规模警察片区划分问题的案例研究验证该方法。结果表明，与基线方法相比，CageBO在性能和效率方面均实现了显著提升。