Recent years have witnessed the emergence of big services, as a large‐scale big data‐centric service model, that resulted from the synergy between powerful computing paradigms (big data processing, service and cloud computing, Internet of Things, etc.). Big services are seen as a heterogeneous combination of physical and virtualized domain‐specific resources, with a huge volume of data and complex functionalities, all encapsulated and offered as services. This complexity of big services (composition units' heterogeneity, cross‐domain orientation, data massiveness), coupled with other environmental factors (cloud dynamicity, providers' policies, customer requirements) makes their management tasks beyond humans' capability. Therefore, endowing big service ecosystems with self‐adaptive behavior is a natural solution. To achieve this goal, this article models big services as autonomic computing systems, and structures their behavioral aspects (functional behavior, quality of service/data levels, management policies) as a multi‐view knowledge graph. To infer useful knowledge (e.g., conflicts between policies) for the autonomic big service's management tasks, we process the big service's knowledge graph (BSKG) via a graph neural network‐based graph embedding model. This latter is reinforced by an incremental learning method, that helps capturing the big services' frequent changes (e.g., QoS deviations, service failures, new policies), and drives autonomic managers to continuously update and enrich their knowledge w.r.t. the managed big service's current state. Finally, a flexible decision mechanism explores the BSKG structure and the latent knowledge, to locate and trigger the appropriate management policies, according to the big service's produced events.