Keeping Pace with Criminals: An Extended Study of Designing Patrol Allocation against Adaptive Opportunistic Criminals

Police patrols are used ubiquitously to deter crimes in urban areas. A distinctive feature of urban crimes is that criminals react opportunistically to patrol officers assignments. Compared to strategic attackers (such as terrorists) with a well-laid out plan, opportunistic criminals are less strategic in planning attacks and more flexible in executing them. In this paper, our goal is to recommend optimal police patrolling strategy against such opportunistic criminals. We first build a game-theoretic model that captures the interaction between officers and opportunistic criminals. However, while different models of adversary behavior have been proposed, their exact form remains uncertain. Rather than simply hypothesizing a model as done in previous work, one key contribution of this paper is to learn the model from real-world criminal activity data. To that end, we represent the criminal behavior and the interaction with the patrol officers as parameters of a Dynamic Bayesian Network (DBN), enabling application of standard algorithms such as EM to learn the parameters. Our second contribution is a sequence of modifications to the DBN representation, that allows for a compact representation of the model resulting in better learning accuracy and increased speed of learning of the EM algorithm when used for the modified DBN. These modifications use marginalization approaches and exploit the structure of this problem. Finally, our third contribution is an iterative learning and planning mechanism that keeps updating the adversary model periodically. We demonstrate the efficiency of our learning algorithm by applying it to a real data set of criminal activity obtained from the police department of University of Southern California (USC) situated in Los Angeles, USA. We project a significant reduction in crime rate using our planning strategy as opposed to the actual strategy deployed by the police department. We also demonstrate the improvement in crime prevention in simulations when we use our iterative planning and learning mechanism compared to just learning once and planing. This work was done in collaboration with the police department of USC.