Data compression technology can reduce the offloading energy consumption of users in mobile edge computing （MEC） by compressing computing tasks. Aiming at the problem that the communication link between the mobile users and the base station is blocked， which has an impact on communication quality， this paper proposes a task offloading scheme based on data compression to meet the requirements of emergency communication and energy-saving offloading in MEC assisted by the unmanned aerial vehicle （UAV） equipped with relay devices and edge servers. Considering constraints such as task compression ratios， system resource and the onboard energy of UAV， we formulate a problem to minimize the sum energy consumption of users. The non-convex optimization problem is modeled as a Markov decision process and the soft actor-critic algorithm based deep reinforcement learning is used to tackle the problem. The simulation results reveal that the proposed scheme achieves better convergence performance and the total energy consumption of users can be reduced by 24.7%—42.2%， compared with the benchmark algorithms.