Wireless local area networks (WLANs) manage multiple access points (APs) and assign scarce radio frequency resources to APs for satisfying traffic demands of associated user devices. This paper considers the channel allocation problem in WLANs that minimizes the mutual interference among APs, and puts forth a learning-based solution that can be implemented in a decentralized manner. We formulate the channel allocation problem as an unsupervised learning problem, parameterize the control policy of radio channels with graph neural networks (GNNs), and train GNNs with the policy gradient method in a model-free manner. The proposed approach allows for a decentralized implementation due to the distributed nature of GNNs and is equivariant to network permutations. The former provides an efficient and scalable solution for large network scenarios, and the latter renders our algorithm independent of the AP reordering. Empirical results are presented to evaluate the proposed approach and corroborate theoretical findings.