Using feedback signals from the environment, a reinforcement learning (RL) system typically discovers action policies that recommend actions effective to the states based on a Q-value function. However, uncertainties over the estimation of the Q-values can delay the convergence of RL. For fast RL convergence by accounting for such uncertainties, this paper proposes several enhancements to the estimation and learning of the Q-value using a self-organizing neural network. Specifically, a temporal difference method known as Q-learning is complemented by a Q-value Polarization procedure, which contrasts the Q-values using feedback signals on the effect of the recommended actions. The polarized Q-values are then learned by the self-organizing neural network using a Bi-directional Template Learning procedure. Furthermore, the polarized Qvalues are in turn used to adapt the reward vigilance of the ART-based self-organizing neural network using a Bi-directional Adaptation procedure. The efficacy of the resultant system called Fast Learning (FL) FALCON is illustrated using two singletask problem domains with large MDPs. The experiment results from these problem domains unanimously show FL-FALCON converging faster than the compared approaches.