Public health organizations need to decide how best to prioritize and target interventions in the most effective manner, given many candidate locations but a limited budget. We consider learning from historical opioid overdose events to predict where to intervene among many candidate spatial regions. Recent work has suggested performance metrics that grade models by how well they recommend a top-K set of regions, computing in hindsight the fraction of events in the actual top-K regions that are covered by the recommendation. We show how to directly optimize such metrics, using advances in perturbed optimizers that allow end-to-end gradient-based training. Experiments suggest that on real opioid-related overdose events from 1620 census tracts in Massachusetts, our end-to-end neural approach selects 100 tracts for intervention better than purpose-built statistical models and tough-to-beat historical baselines.