Data compression technology is able to reduce data size, which can be applied to lower the cost of task offloading in mobile edge computing (MEC). This paper addresses the practical challenges for robust trajectory and scheduling optimization based on data compression in the unmanned aerial vehicle (UAV)-assisted MEC, aiming to minimize the sum energy cost of terminal users while maintaining robust performance during UAV flight. Considering the non-convexity of the problem and the dynamic nature of the scenario, the optimization problem is reformulated as a Markov decision process. Then, a randomized ensembled double Q-learning (REDQ) algorithm is adopted to solve the issue. The algorithm allows for higher feasible update-to-data ratio, enabling more effective learning from observed data. The simulation results show that the proposed scheme effectively reduces the energy consumption while ensuring flight robustness. Compared to the PPO and A2C algorithms, energy consumption is reduced by approximately $21.9\%$ and $35.4\%$, respectively. This method demonstrates significant advantages in complex environments and holds great potential for practical applications.