  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.
