Symmetric bi-manual manipulation is an essential skill in on-orbit operations due to its potent load capacity. Previous works have applied compliant control to maintain the stability of manipulations. However, traditional methods have viewed motion planning and compliant control as two separate modules, which can lead to conflicts with the simultaneous change of the desired trajectory and impedance parameters in the presence of external forces and disturbances. Additionally, the joint usage of these two modules requires experts to manually adjust parameters. To achieve high efficiency while enhancing adaptability, we propose a novel Learning-based Adaptive Compliance algorithm (LAC) that improves the efficiency and robustness of symmetric bi-manual manipulation. Specifically, the algorithm framework integrates desired trajectory generation and impedance-parameter adjustment under a unified framework to mitigate contradictions and improve efficiency. Second, we introduce a centralized Actor-Critic framework with LSTM networks preprocessing the force states, enhancing the synchronization of bi-manual manipulation. When evaluated in dual-arm peg-in-hole assembly experiments, our method outperforms baseline algorithms in terms of optimality and robustness.