The current document is directed to an administrator-monitored reinforcement-learning-based application manager that can be deployed in various different computational environments to manage the computational environments with respect to one or more reward-specified goals. Certain control actions undertaken by the administrator-monitored reinforcement-learning-based application manager are first proposed, to one or more administrators or other users, who can accept or reject the proposed control actions prior to their execution. The reinforcement-learning-based application manager can therefore continue to explore the state/action space, but the exploration can be parametrically constrained as well as by human-administrator oversight and intervention.