As network architecture becomes complex and the user requirement gets diverse, the role of efficient network resource management becomes more important. However, existing throughput-optimal scheduling algorithms such as the max-weight algorithm suffer from poor delay performance. In this paper, we present reinforcement learning-based network scheduling algorithms for a single-hop downlink scenario which achieve throughput-optimality and converge to minimal delay. To this end, we first formulate the network optimization problem as a Markov decision process (MDP) problem. Then, we introduce a new state-action value function called $Q^{+}$ -function and develop a reinforcement learning algorithm called $Q^{+}$ -learning with UCB (Upper Confidence Bound) exploration which guarantees small performance loss during a learning process. We also derive an upper bound of the sample complexity in our algorithm, which is more efficient than the best known bound from Q-learning with UCB exploration by a factor of $\gamma ^{2}$ where $\gamma$ is the discount factor of the MDP problem. Finally, via simulation, we verify that our algorithm shows a delay reduction of up to 40.8% compared to the max-weight algorithm over various scenarios. We also show that the Q⁺-learning with UCB exploration converges to an $\epsilon$ -optimal policy 10 times faster than Q-learning with UCB.