The high agility and maneuverability of the unmanned aerial vehicles (UAVs) provide a unique opportunity to carry communications and edge-computing facilities on board to serve mobile users in the cellular networks. An important problem would be to maximize the average aggregate quality-of-experience of all users over time slots. However, this is a non-convex, nonlinear and mixed discrete optimization problem, which is difficult to solve and obtain the optimal solution. We thus propose a deep reinforcement learning algorithm to solve this problem by considering UAV path planning, user assignment, bandwidth and computing resource assignment. The UAVs and base stations are to serve mobile users in multiple continuous time slots, and machine learning is leveraged to facilitate joint resource allocation and path planning in provisioning UAV-assisted edge computing. We compare the performance of our proposal with two baseline cases through simulations 1) with fixed UAV locations and 2) without UAVs. We demonstrate that the deep reinforcement learning algorithm performs better than these two baseline cases.