We employ a variant of max-violation (Huang et al., 2012) as our training objective, in which parameters are updated based on the worst mistake found during search, rather than the first mistake as performed in the early update perceptron algorithm (Collins and Roark, 2004).
given a training instance (w, y) where w is an input sentence and y is its gold derivation, i.e., a sequence of actions representing the gold parse tree for w, we seek for the step j * where the difference of the scores is the largest: Then, we define the following hinge-loss function: wherein we consider the subset of sub-derivations B j * ⊂ B j * consisting of those scored higher than ρ θ (y j * 0 ): Unlike Huang et al.