Learning Interpretable Error Functions for Combinatorial Optimization Problem Modeling

TL;DR

This paper introduces a novel method to automatically learn interpretable error functions for constraints in combinatorial optimization, enhancing problem modeling by leveraging specialized neural networks.

Contribution

It presents the first approach to automatically learn error functions for hard constraints using Interpretable Compositional Networks, improving scalability and interpretability.

Findings

Learned functions scale to high-dimensional problems.

Functions perform well over incomplete solution spaces.

System successfully models five different types of constraints.

Abstract

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.