Many studies have been devoted to channel allocation for backhaul links in wireless mesh networks. Among them, a game-theoretic approach proposed by Yen and Dai is promising for the ability to self-stabilize to a valid solution in a decentralized manner. However, game-based solutions are generally not optimal. Furthermore, Yen and Dai's approach did not fully utilize all available channels, wasting scarce bandwidth resource. In this paper, we propose two learning-based approaches to enhance the prior work. One uses Spatial Adaptive Play (SAP) for agents to learn best probability distributions on their possible channel selections. The other based on multi-agent reinforcement learning (MARL) algorithm allows each agent to find out its best selection over time. Simulation results reveal that the proposed approaches do improve the game-based solutions in terms of the number of operative links after channel allocations.