  In Semantic Dependency Parsing (SDP), semantic relations form directed
acyclic graphs, rather than trees. We propose a new iterative predicate
selection (IPS) algorithm for SDP. Our IPS algorithm combines the graph-based
and transition-based parsing approaches in order to handle multiple semantic
head words. We train the IPS model using a combination of multi-task learning
and task-specific policy gradient training. Trained this way, IPS achieves a
new state of the art on the SemEval 2015 Task 18 datasets. Furthermore, we
observe that policy gradient training learns an easy-first strategy.
