This paper studies the trajectory optimization problem for an aerial vehicle with the mission of flying between a pair of given initial and final locations. The objective is to minimize the travel time of the aerial vehicle ensuring that the communication connectivity constraint required for the safe operation of the aerial vehicle is satisfied... We consider two different criteria for the connectivity constraint of the aerial vehicle which leads to two different scenarios. In the first scenario, we assume that the maximum continuous time duration that the aerial vehicle is out of the coverage of the ground base stations (GBSs) is limited to a given threshold. In the second scenario, however, we assume that the total time periods that the aerial vehicle is not covered by the GBSs is restricted. Based on these two constraints, we formulate two trajectory optimization problems. To solve these non-convex problems, we use an approach based on the double Q-learning method which is a model-free reinforcement learning technique and unlike the existing algorithms does not need perfect knowledge of the environment. Moreover, in contrast to the well-known Q-learning technique, our double Q-learning algorithm does not suffer from the over-estimation issue. Simulation results show that although our algorithm does not require prior information of the environment, it works well and shows near optimal performance. (read more)