The transition towards full network virtualization will see services for smart ecosystems including smart metering, healthcare and transportation among others, being deployed as Service Function Chains (SFCs) comprised of an ordered set of virtual network functions. However, since such services are usually deployed in remote cloud networks, the SFCs may transcend multiple domains belonging to different Infrastructure Providers (InPs), possibly with differing policies regarding billing and Quality-of-service (QoS) guarantees. Therefore, efficiently allocating the exhaustible network resources to the different SFCs while meeting the stringent requirements of the services such as delay and QoS among others, remains a complex challenge, especially under limited information disclosure by the InPs. In this work, we formulate the SFC deployment problem across multiple domains focusing on delay constraints, and propose a framework for SFC orchestration which adheres to the privacy requirements of the InPs. Then, we propose a Reinforcement Learning (RL) basedalgorithm for partitioning the SFC request across the different InPs while considering service reliability across the participating InPs. Such RL based algorithms have the intelligence to infer undisclosed InP information from historical data obtained from past experiences. Simulation results, considering both online and offline scenarios, reveal that the proposed algorithm results in