A differentially private security system communicatively coupled to a database storing restricted data receives a database query from a client. The database query includes a relation specifying a set of data in the database upon which to perform the query and privacy parameters associated with the query. The differentially private security system determines a worst-case privacy spend for the query based on the privacy parameters and the relation. The differentially private security system performs the query upon the set of data specified by the relation and decrements the determined worst-case privacy spend from a privacy budget associated with the client. The differentially private security system records the worst-case privacy spend and the query at a log and determines a privacy budget refund based on queries recorded in the log. The differentially private security system applies the determined privacy budget refund to the privacy budget associated with the client.