This paper addresses the use of Big Data and machine learning based analytics to the real-time management of Internet scale Quality-of-Service Route Optimisation with the help of an overlay network. Based on the collection of large amounts of data sampled each $2$ minutes over a large number of source-destinations pairs, we show that intercontinental Internet Protocol (IP) paths are far from optimal with respect to Quality of Service (QoS) metrics such as end-to-end round-trip delay. We therefore develop a machine learning based scheme that exploits large scale data collected from communicating node pairs in a multi-hop overlay network that uses IP between the overlay nodes themselves, to select paths that provide substantially better QoS than IP. The approach inspired from Cognitive Packet Network protocol, uses Random Neural Networks with Reinforcement Learning based on the massive data that is collected, to select intermediate overlay hops resulting in significantly better QoS than IP itself. The routing scheme is illustrated on a $20$-node intercontinental overlay network that collects close to $2\times 10^6$ measurements per week, and makes scalable distributed routing decisions. Experimental results show that this approach improves QoS significantly and efficiently in a scalable manner.