As the computing continuum increasingly becomes the default deployment infrastructure for modern systems, the demand for a programming model capable of meeting the requirements for developing software systems on such infrastructures also grows. This model must provide abstractions to manage the high level of dynamism inherent in these environments, particularly addressing the autonomous management of stateful service placement across large-scale edge-cloud continuum infrastructures. To address this issue, we explore the concept of self-distributing systems – a machine-centric approach to deal with the complexity of designing distributed systems. We take a step further and have the system decide on distributed design decisions at runtime as unexpected changes and events occur, leaving the system responsible for reacting quickly and accurately as a response to such changes. This paper presents the application of a multi-agent learning approach to learn how to distribute stateful services across the continuum. We demonstrate the efficiency of such a method in a local testbed. We compare our results against a multi-armed bandits approach, pinpointing the strengths and weaknesses of the two approaches.