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

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 fully integrate integer programming solvers into neural network architecture by providing gradient update rules for 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 in multiple ways: on random constraints, on solving Knapsack instances from their description in natural language, and on a popular computer vision benchmark regarding keypoint matching.