Cloud computing generates a proper computing platform and facilitates optimizing with the utilization of infrastructure resources, increases flexibility, and decreases deployment time. Interoperability is one of the major challenges to be studied for ensuring seamless access and sharing of services and resources. Containers have developed into the most dependable and lightweight platform for virtualization to deliver cloud services that offer flexible sorting, scalability, and portability. This paper presents energy-efficient data migration approach using hybrid optimized deep learning in a heterogeneous cloud. Simulation of the cloud is carried out with Physical Machines (PM), container, and Virtual Machines (VM) in the cloud. Migration application is done with proposed Taylor Lion-based Poor and Rich Optimization (Taylor Lion-based PRO), wherein load is found by Actor Critic Neural Network (ACNN). Moreover, objective functions utilized are agility, migration time, predicted load, demand, transmission cost, resource capacity, energy consumption, as well as reputation. Here, Taylor Lion-based PRO is formed by hybridization of the Taylor series along Lion Optimization Algorithm (LOA), and Poor and Rich Optimization (PRO). Furthermore, the performance of data migration concerning interoperability is carried out with three performance metrics, like load, resource capacity, and energy consumption of 0.006, 0.364, and 0.281.