  The hardness of combinatorial optimization (CO) problems hinders collecting
solutions for supervised learning. However, learning neural networks for CO
problems is notoriously difficult in lack of the labeled data as the training
is easily trapped at local optima. In this work, we propose a simple but
effective annealed training framework for CO problems. In particular, we
transform CO problems into unbiased energy-based models (EBMs). We carefully
selected the penalties terms so as to make the EBMs as smooth as possible. Then
we train graph neural networks to approximate the EBMs. To prevent the training
from being stuck at local optima near the initialization, we introduce an
annealed loss function. An experimental evaluation demonstrates that our
annealed training framework obtains substantial improvements. In four types of
CO problems, our method achieves performance substantially better than other
unsupervised neural methods on both synthetic and real-world graphs.
