Unsupervised Learning Permutations for TSP using Gumbel-Sinkhorn Operator

Yimeng Min, Carla Gomes

Keywords: Optimal Transport, TSP, Entropy Regularization, Unsupervised learning

TL;DR: Using optimal transport method to learn algorithmic prior for Travelling Salesman Problem

Abstract: The Machine Learning community has recently shown a growing interest in Optimal Transport (OT). Methods that leverage entropy regularization based on OT have proven especially effective for various tasks, including ranking, sorting, and solving jigsaw puzzles. In our study, we broaden the application of entropy regularization methods to address the NP-hard Travelling Salesman Problem (TSP). We first formulate TSP as identifying the permutation of a Hamiltonian Cycle with the shortest length. Following this, we establish the permutation representation using the Gumbel-Sinkhorn operator with entropic regularization. Our findings indicate a balance between entropy and generalization. We further discuss how to generalize across different hardnesses.

Submission Number: 78