Future Internet will be highly heterogeneous supporting a multitude of access technologies with overlapping coverages. The automation and optimization of network operations like resource, mobility or QoS management in such a multi-access and multi-operator environment becomes a very challenging but vital task in order to ensure smooth network operation and user satisfaction. Cognitive network management is seen as the solution for this. However, any self* mechanism designed for small-scale networks and requiring an accurate view of the whole network status for decision-making will not be able to meet the future needs. In this paper, we propose a novel multi-access network management architecture targeted for large heterogeneous multi-access and multi-operator networks. The architecture introduces hierarchy to network management to ensure scalability. We also present results obtained from a case example of the proposed decision-making solution implemented to our cognitive network testbed