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

Reversible Action Design for Combinatorial Optimization with Reinforcement Learning