CiviVolunteer front-end assignment listing
I assume that by front-end user you mean that the user doesn't have the "Access CiviCRM" permission?

Options for viewing the roster are outlined in the still-nascent documentation. Summary:


Using the admin menu, go to Volunteers > Manage Volunteer Projects (on Drupal the URL looks something like  https://example.org/civicrm/vol/#/volunteer/manage). Note: this screen does not require "Access CiviCRM."
Find the Project of interest, and click "View Volunteer Roster."