This paper studies the uplink and downlink power allocation for interactive augmented reality (AR) services, where the live video captured by an AR device is uploaded to the network edge, and then the augmented video is subsequently downloaded. By modeling the AR transmission process as a tandem queuing system, we derive an upper bound for the probabilistic quality of service (QoS) requirement concerning end-to-end latency and reliability. The resource allocation under the QoS requirement results in a functional optimization problem. To address it, we design a deep neural network to learn the power allocation policy, leveraging the optimal power allocation structure to enhance learning performance. Simulation results demonstrate that the proposed method effectively reduces transmit power while meeting the QoS requirement.