Variational Annealing on Graphs for Combinatorial Optimization
This work improves combinatorial optimization methods for researchers and practitioners, though it is incremental as it builds on existing probabilistic and autoregressive techniques.
The paper tackles performance limitations in combinatorial optimization by addressing the assumption of independent solution variables, showing that an autoregressive approach with subgraph tokenization and annealed entropy regularization yields superior results on many problems.
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.