Learning Combinatorial Node Labeling Algorithms

TL;DR

This paper introduces a neural network-based approach using reinforcement learning to efficiently solve complex graph labeling problems like graph coloring and vertex cover, outperforming classical heuristics.

Contribution

It presents a novel neural architecture with inductive biases and reinforcement learning for combinatorial node labeling, achieving superior solutions and generalization.

Findings

Outperforms classical greedy heuristics in graph coloring

Achieves faster solutions on large graphs with tens of thousands of vertices

Generalizes to other problems like minimum vertex cover

Abstract

We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning, specifically policy gradients, which gives us both a greedy and a probabilistic policy. Our architecture builds on a graph attention network and uses several inductive biases to improve solution quality. Our learned deterministic heuristics for graph coloring give better solutions than classical degree-based greedy heuristics and only take seconds to apply to graphs with tens of thousands of vertices. Moreover, our probabilistic policies outperform all greedy state-of-the-art coloring baselines and a machine learning baseline. Finally, we show that our approach also generalizes to other problems by evaluating it on minimum vertex cover and outperforming two greedy heuristics.