Quantitatively, we show a variety of bounds relating the number of mistakes to well-known combinatorial dimensions.

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.

However, achieving such an assumption is non-trivial, leading to the following two aspects of challenges. On the one hand, it is challenging to design a model with enough capacity with limited computational resources, andexisting models areusually tailored forspecific problems which require heavytrailand-error [25,57,59].

Experimental results showthattheproposed metriclearning algorithm improves both certified robust errors and empirical robust errors (errors under adversarial attacks).