Fit The Right NP-Hard Problem: End-to-end Learning of Integer Programming Constraints

Anselm Paulus, Michal Rolinek, Vít Musil, Brandon Amos, Georg Martius

Keywords: integer programming, discrete optimization, hybrid architectures, learning constraints

TL;DR: We propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers.

Abstract:

Bridging logical and algorithmic reasoning with modern machine learning
techniques is a fundamental challenge with potentially transformative impact.
On the algorithmic side, many NP-Hard problems can be expressed as integer
programs, in which the constraints play the role of their ``combinatorial
specification''. In this work, we aim to integrate integer programming solvers
into neural network architectures by providing loss functions for \emph{both}
the objective and the constraints. The resulting end-to-end trainable
architectures have the power of jointly extracting features from raw data and
of solving a suitable (learned) combinatorial problem with state-of-the-art
integer programming solvers. We experimentally validate our approach on
artificial datasets created from random constraints, and on solving
\textsc{Knapsack} instances from their description in natural language.