For routing closures in package designs, net order is critical due to complex design rules and severe wire congestion. However, existing solutions are deliberatively designed using heuristics and are difficult to adapt to different design requirements unless updating the algorithm. This work presents a novel deep learning-based routing framework that can keep improving by accumulating data to accommodate increasingly complex design requirements. Based on the initial routing results, we apply deep learning to concurrent detailed routing to deal with the problem of net ordering decisions. We use multi-agent deep reinforcement learning to learn routing schedules between nets. We regard each net as an agent, which needs to consider the actions of other agents while making pathing decisions to avoid routing conflict. Experimental results on industrial package design show that the proposed framework can improve the number of design rule violations by 99.5% and the wirelength by 2.9% for initial routing.