# Learning Interpretable Error Functions for Combinatorial Optimization Problem Modeling

arXiv: https://arxiv.org/abs/2002.09811 · HTML: https://mlsanity.com/paper/2002.09811/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Terrain Analysis in StarCraft 1 and 2 as Combinatorial Optimization](https://mlsanity.com/paper/2205.08683/) (2022)

## Abstract (arXiv)

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.