In this paper, a Deep Q-Network (DQN) based multi-agent multi-user power allocation algorithm is proposed for hybrid networks composed of radio frequency (RF) and visible light communication (VLC) access points (APs). The users are capable of multihoming, which can bridge RF and VLC links for accommodating their bandwidth requirements. By leveraging a non-cooperative multi-agent DQN algorithm, where each AP is an agent, an online power allocation strategy is developed to optimize the transmit power for providing users' required data rate. Our simulation results demonstrate that DQN's median convergence time training is 90% shorter than the Q-Learning (QL) based algorithm. The DQN-based algorithm converges to the desired user rate in half duration on average while converging with the rate of 96.1% compared to the QL-based algorithm's convergence rate of 72.3% Additionally, thanks to its continuous state-space definition, the DQN-based power allocation algorithm provides average user data rates closer to the target rates than the QL-based algorithm when it converges.