Erd os GNN [29] is a novel framework with unsupervised learning, however, its main limitation is that this framework is incapable of handling constraints beyond simple node constraints. Following the implementation from [39], the job nodes are scheduled in sequential order with PPO-Single. Herestateisthe current DAGGk with atimestamp, and some of the nodes are already scheduled by the current timestamp. Torepresent the current state of the problem, the finished nodes, running nodes and unscheduled nodes are marked by different node 15 attributes, so that the state information is fully encoded by the nodes and edges ofGk. After anode finishes, itwillfreesome resources, and sometimes add some available nodes to be scheduled.

We would also like to discuss the limitations of the approaches including ours. As shown in Tab. 4, the PPO-Single that serves as a baseline in our paper is designed following As shown in Tab. 4, NerRewritter is most general because it can be viewed as a learning-based local It is also worth noting that there are some problems that are beyond our knowledge to tackle, e.g. the expression simplify problem, and it may requires experts with specific domain We have discussed the model details of PPO-BiHyb in Sec. 4, and in this section, we discuss the DAG. Considering the structure of DAG, we design two GCNs: the first GCN processes the original DAG, and the second GCN processes the DAG with all edges reversed. The predicted doubly-stochastic matrix by SK is processed by considering the partial matching matrix. Graph-level features are obtained via attention pooling, which are fed to the critic net.