With the rise of next-generation communication technology, particularly the deep integration of 6th Generation Mobile Networks (6G), the Internet of Things (IoT), and Artificial Intelligence (AI), edge computing is gradually emerging as a cutting-edge computing paradigm. In the edge computing architecture, an appropriate task offloading strategy is crucial for processing tasks with high data sensitivity requirements. This paper combines the Q-learning algorithm in reinforcement learning with optimal stopping theory to develop a new task offloading strategy. It trains intelligent agents to learn offloading decisions and, based on the optimal stopping theory, establishes criteria to optimize these decisions, ultimately achieving efficient and accurate offloading. Experimental verification shows that this strategy significantly reduces the number of iterations and effectively lowers system energy consumption.