  Combinatorial optimization problem (COP) over graphs is a fundamental
challenge in optimization. Reinforcement learning (RL) has recently emerged as
a new framework to tackle these problems and has demonstrated promising
results. However, most RL solutions employ a greedy manner to construct the
solution incrementally, thus inevitably pose unnecessary dependency on action
sequences and need a lot of problem-specific designs. We propose a general RL
framework that not only exhibits state-of-the-art empirical performance but
also generalizes to a variety class of COPs. Specifically, we define state as a
solution to a problem instance and action as a perturbation to this solution.
We utilize graph neural networks (GNN) to extract latent representations for
given problem instances for state-action encoding, and then apply deep
Q-learning to obtain a policy that gradually refines the solution by flipping
or swapping vertex labels. Experiments are conducted on Maximum $k$-Cut and
Traveling Salesman Problem and performance improvement is achieved against a
set of learning-based and heuristic baselines.
