Reviews: A Primal Dual Formulation For Deep Learning With Constraints

The paper converts the constrained optimization problem to min-max optimization using Lagrangian function. To show the efficacy of the model, three experiments are conducted in 5.1 SRL, 5.2 NER and 5.3 Fine grained entity typing. The paper brings in a structured way of training with output constraints. However, I am not sure how much gain this model has on top of fixed weight on constraints (Metha et al 2018 & Diligenti et al 2017) with the provided experiments. Also while the experiments seem convincing as itself, it is hard to see how much significance this work brings in as the baselines significantly differ with related work. Also, it would give a better picture of this method if the paper could provide more analysis: an analysis on convergence, an analysis on experiment results on why more labeled data sometimes hurt, etc. [originality ] 1. The full Lagrangian expression and linking the output constraint to the model parameter and optimizing them with subgradient seems novel. However, how exactly the authors formulate f(w) is unclear to me. Is it just following the way Diligenti 2017 does it?