Fairness of predictive policing as a dynamic environment

Predictive policing can be seen as an allocation problem, where we allocate police patrols to different areas trying to minimize crimes. The fairness of allocation problems has been studied by [1], proposing a metric of fairness and a fair algorithm for learning in this problem setting. The assumption of the study is that the environment is static, which is not the case for predictive policing, where the allocation of police patrols changes the underlying distribution of crimes for the next observation. We study the problem of fairness in this dynamic environment extension.