As an emerging computing paradigm, edge computing offers computing resources closer to the data sources, helping to improve the service quality of many real-time applications. A crucial problem is designing a rational pricing mechanism to maximize the revenue of the edge computing service provider (ECSP). However, prior works have considerable limitations: clients are static and are required to disclose their preferences, which is impractical in reality. However, previous works assume user privacy information to be known or consider the number of users in edge scenarios to be static. To address this issue, we propose a novel sequential computation offloading mechanism, where the ECSP posts prices of computing resources with different configurations to clients in turn. Clients independently choose which computing resources to purchase and how to offload based on their prices. Then Egret, a deep reinforcement learning-based approach that achieves maximum revenue, is proposed. Egret determines the optimal price and visiting orders online without considering clients' preferences. Experimental results show that the revenue of ECSP in Egret is only 1.29\% lower than Oracle and 23.43\% better than the state-of-the-art when the client arrives dynamically.