  A general framework of unsupervised learning for combinatorial optimization
(CO) is to train a neural network (NN) whose output gives a problem solution by
directly optimizing the CO objective. Albeit with some advantages over
traditional solvers, the current framework optimizes an averaged performance
over the distribution of historical problem instances, which misaligns with the
actual goal of CO that looks for a good solution to every future encountered
instance. With this observation, we propose a new objective of unsupervised
learning for CO where the goal of learning is to search for good initialization
for future problem instances rather than give direct solutions. We propose a
meta-learning-based training pipeline for this new objective. Our method
achieves good empirical performance. We observe that even just the initial
solution given by our model before fine-tuning can significantly outperform the
baselines under various evaluation settings including evaluation across
multiple datasets, and the case with big shifts in the problem scale. The
reason we conjecture is that meta-learning-based training lets the model be
loosely tied to each local optima for a training instance while being more
adaptive to the changes of optimization landscapes across instances.
