Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization

Yimeng Min, Carla P Gomes

Keywords: Structural Inductive Bias, Travelling Salesman Problem, Combinatorial Optimization, Unsupervised Learning, Non-Autoregressive Models, Permutation Learning, Graph Neural Networks, Gumbel-Sinkhorn, Ensemble Methods

TL;DR: We present an unsupervised, non-autoregressive method that learns permutation matrices to solve the TSP without search, achieving competitive results using structural inductive bias and Hamiltonian cycle ensembles.

Abstract: We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the model learns to approximate permutation matrices via continuous relaxations. Our unsupervised approach achieves competitive performance against classical heuristics, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without sequential decision-making.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 599