Variational Annealing on Graphs for Combinatorial Optimization

Sebastian Sanokowski, Wilhelm Franz Berghammer, Sepp Hochreiter, Sebastian Lehner

Keywords: Combinatorial Optimization, Entropy Regularization, Graph Neural Networks, Statistical Mechanics

Abstract: Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances. Our results corroborate that an autoregressive approach which captures statistical dependencies among solution variables yields superior performance on many popular CO problems. We introduce Subgraph Tokenization in which the configuration of a set of solution variables is represented by a single token. This tokenization technique alleviates the drawback of the long sequential sampling procedure which is inherent to autoregressive methods without sacrificing expressivity. Importantly, we theoretically motivate an annealed entropy regularization and show empirically that it is essential for efficient and stable learning.

Submission Number: 12601