The current document is directed to reinforcement-learning-based management-system agents that control distributed applications and the infrastructure environments in which they run. Management-system agents are initially trained in simulated environments and specialized training environments before being deployed to live, target distributed computer systems where they operate in a controller mode in which they do not explore the control-state space or attempt to learn better policies and value functions, but instead produce traces that are collected and stored for subsequent use. Each deployed management-system agent is associated with a twin training agent that uses the collected traces produced by the deployed management-system agent for optimizing its policy and value functions. To further ensure safe operational control of the environment, the management-system agents employ lookahead planning, action budgets, and action constraints to forestall issuance, by management-system controllers, of potentially deleterious actions.