Differentiation of Blackbox Combinatorial Solvers

TL;DR

This paper introduces a method for differentiating through blackbox combinatorial solvers, enabling their integration into neural networks for solving complex problems like TSP, matching, and shortest path.

Contribution

It presents an efficient backward pass technique for blackbox combinatorial solvers, allowing end-to-end training of neural architectures incorporating these solvers.

Findings

Successfully integrated Gurobi, Blossom V, and Dijkstra into neural architectures.

Demonstrated the approach on TSP, matching, and shortest path problems.

Provided theoretical and experimental validation of the method.

Abstract

Achieving fusion of deep learning with combinatorial algorithms promises transformative changes to artificial intelligence. One possible approach is to introduce combinatorial building blocks into neural networks. Such end-to-end architectures have the potential to tackle combinatorial problems on raw input data such as ensuring global consistency in multi-object tracking or route planning on maps in robotics. In this work, we present a method that implements an efficient backward pass through blackbox implementations of combinatorial solvers with linear objective functions. We provide both theoretical and experimental backing. In particular, we incorporate the Gurobi MIP solver, Blossom V algorithm, and Dijkstra's algorithm into architectures that extract suitable features from raw inputs for the traveling salesman problem, the min-cost perfect matching problem and the shortest path problem. The code is available at https://github.com/martius-lab/blackbox-backprop.