Spatiotemporal crime prediction and fairness-constrained spatial optimization with deep reinforcement learning for patrol region design

• Presents a unified framework for spatio-temporal crime prediction and patrol allocation. • Proposes MRD-MCLP, a patrol location model balancing coverage and fairness. • Develops a deep reinforcement learning algorithm to efficiently solve MRD-MCLP. Existing police resource allocation relies on the prediction of historical crime hotspots, which is difficult to balance the overall effectiveness and regional fairness, resulting in an imbalance in the allocation of resources and difficulty in adapting to dynamic security needs. Taking Los Angeles as the study area, this study first constructs an XGBoost regression prediction model to quantify the future crime risk of each area based on the crime location and time information in the historical crime data, and then introduces the minimum regional disparity (MRD) constraint on the basis of which the fairness indicator is integrated into the optimization framework of patrol region allocation. Meanwhile, this study innovatively introduces a deep reinforcement learning method to improve the model’s solution efficiency and adaptability under complex constraints by interacting with the environment through a policy network. The experimental results show that the MRD fairness model significantly improves resource allocation fairness. Compared with the maximum coverage model, the Gini coefficient and coefficient of variation decrease by 42.56 % and 57.59 %, respectively, and the Jain’s fairness index simultaneously increases by 94.33 %. Regarding patrol region configuration, the proposed method decreases resource redundancy by 66.62 % and increases the spatial balance of facility distribution by 7.5 %, thereby effectively improving resource utilization and spatial layout rationality. Additionally, the deep reinforcement learning (DRL) strategy substantially reduces computational time compared to the classical mixed-integer programming solver, efficiently meeting dual constraints of fairness and coverage effectiveness. In summary, this study integrates MRD constraints and DRL to achieve equitable, efficient policing resource allocation, providing a practical and effective technical pathway for addressing fairness and efficiency demands.