Learning Interpretable Error Functions for Combinatorial Optimization
  Problem Modeling
  In Constraint Programming, constraints are usually represented as predicates
allowing or forbidding combinations of values. However, some algorithms exploit
a finer representation: error functions. Their usage comes with a price though:
it makes problem modeling significantly harder. Here, we propose a method to
automatically learn an error function corresponding to a constraint, given a
function deciding if assignments are valid or not. This is, to the best of our
knowledge, the first attempt to automatically learn error functions for hard
constraints. Our method uses a variant of neural networks we named
Interpretable Compositional Networks, allowing us to get interpretable results,
unlike regular artificial neural networks. Experiments on 5 different
constraints show that our system can learn functions that scale to high
dimensions, and can learn fairly good functions over incomplete spaces.
