Fresh Start Act of 2018 This bill establishes a process to expunge records related to certain nonviolent criminal offenses. It defines the nonviolent offenses eligible for expungement; it establishes qualifications for an eligible offender; and it sets forth procedures for filing an expungement petition. The bill increases by 5% the allocation of funds under the Edward Byrne Memorial Justice Assistance Grant (JAG) Program for a state that implements expungement procedures substantially similar to this bill. It decreases by 5% the JAG allocation for a state that fails to enact substantially similar expungement procedures.