Abstract: The current document is directed to methods and systems that automatically instantiate complex distributed applications by deploying distributed-application instances across the computational resources of one or more distributed computer systems and that automatically manage instantiated distributed applications. Automatic deployment of multiple instances of a distributed application across computational resources, such as distribution of microservices of a microservice-based application across one or more distributed computer systems, and scaling of instantiated distributed applications are computationally difficult optimization problems that are not amenable to traditional centralized approaches. The current document discloses decentralized, distributed automated methods and systems that instantiate and manage distributed applications. Reinforcement-learning-based agents are installed within the computational resources of one or more distributed computer systems.