It is widely acknowledged that the development of traditional terrestrial communication technologies cannot provide all users with fair and high quality services due to scarce network resources and limited coverage areas. To complement the terrestrial connection, especially for users in rural, disaster-stricken, or other difficult-to-serve areas, satellites, UAVs, and balloons have been utilized to relay communication signals. On this basis, SAGINs have been proposed to improve the users' QoE. However, compared with existing networks such as ad hoc networks and cellular networks, SAGINs are much more complex due to the various characteristics of three network segments. To improve the performance of SAGINs, researchers are facing many unprecedented challenges. In this article, we propose the AI technique to optimize SAGINs, as the AI technique has shown its predominant advantages in many applications. We first analyze several main challenges of SAGINs and explain how these problems can be solved by AI. Then, we consider the satellite traffic balance as an example and propose a deep learning based method to improve traffic control performance. Simulation results evaluate that the deep learning technique can be an efficient tool to improve the performance of SAGINs.