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：黑盒优化（BBO）在解决复杂决策问题（尤其是警察辖区划分等公共政策领域）中日益重要。然而，其在公共政策制定中的广泛应用受到可行区域定义复杂性和决策高维性的制约。本文提出了一种新颖的BBO框架，称为条件生成黑盒优化（CageBO）。该方法利用条件变分自编码器学习可行决策的分布，实现了原始决策空间与简化无约束潜空间之间的双向映射。CageBO能有效处理公共政策应用中常见的隐式约束，支持在潜空间进行优化，同时在原始空间评估目标函数。我们通过对佐治亚州亚特兰大市大规模警察辖区划分问题的案例研究验证了本方法。结果表明，与基线方法相比，我们的CageBO在性能与效率方面均有显著提升。