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In recent years, with the large-scale deployment of space spacecraft entities and the increase of satellite onboard capabilities, delay/disruption tolerant network (DTN) emerged as a more robust communication protocol than TCP/IP in the case of excessive network dynamics. DTN node buffer management is still an active area of research, as the current implementation of the DTN core protocol still relies on the assumption that there is always enough memory available in different network nodes to store and forward bundles. In addition, the classical queuing theory does not apply to the dynamic management of DTN node buffers. Therefore, this paper proposes a centralized approach to automatically manage cognitive DTN nodes in low earth orbit (LEO) satellite constellation scenarios based on the advanced reinforcement learning (RL) strategy advantage actor-critic (A2C). The method aims to explore training a geosynchronous earth orbit intelligent agent to manage all DTN nodes in an LEO satellite constellation scenario. The goal of the A2C agent is to maximize delivery success rate and minimize network resource consumption cost while considering node memory utilization. The intelligent agent can dynamically adjust the radio data rate and perform drop operations based on bundle priority. In order to measure the effectiveness of applying A2C technology to DTN node management issues in LEO satellite constellation scenarios, this paper compares the trained intelligent agent strategy with the other two non-RL policies, including random and standard policies. Experiments show that the A2C strategy balances delivery success rate and cost, and provides the highest reward and the lowest node memory utilization.