###### Abstract  
Many applications in Multi-access Edge Computing (MEC) consist of interdependent tasks where the output of some tasks is the input of others. Most of the existing research on computational offloading does not consider the dependency of the task and uses convex relaxation or heuristic algorithms to solve the offloading problem, which lacks adaptability and is not suitable for computational offloading in the dynamic environment of fast fading channels. Therefore, in this paper, the optimization problem is modeled as a Markov Decision Process (MDP) in multi-user and multi-server MEC environments, and the dependent tasks are represented by Directed Acyclic Graph (DAG). Combined with the Soft Actor-Critic (SAC) algorithm in Deep Reinforcement Learning (DRL) theory, an intelligent task offloading scheme is proposed. Under the condition of resource constraint, each task can be offloaded to the corresponding MEC server through centralized control, which greatly reduces the service delay and terminal energy consumption. The experimental results show that the algorithm converges quickly and stably, and its optimization effect is better than existing methods, which verifies the effectiveness of the algorithm. multi-access edge computing; directed acyclic graph; deep reinforcement learning; offloading strategy +
Footnote †: journal: Applied Sciences  
In addition, many works have only considered the offloading problem in the single-server scenario but have not studied the multiserver MEC scenario. In practice, a densely deployed multiple MEC server can perform uninterrupted task offloading to meet the service demand [3]. To cover these research gaps, we proposed a Soft Actor-Critic-based Dependent Task Offloading (SACDTO) strategy; designed a new objective function in the multi-user, multi-server MEC environment; and modeled the optimization problem as a Markov Decision Process (MDP). The dependent tasks are represented by Directed Acyclic Graphs (DAG), where vertices and edges denote tasks and their dependency, respectively. In addition, we utilize the Soft Actor-Critic (SAC) method based on a maximum entropy reinforcement learning framework. Under resource constraints, we can offload tasks to the specified server number. A large number of simulation experiments show that SACDTO can drastically reduce the service delay and terminal energy consumption. The SACDTO strategy learns to make proper offloading decisions by directly interacting with the environment. The chief contributions of this paper are summarized as follows:  
* We design an MDP to accurately model the dependent task offloading problem with well-designed state space, action space, and reward function. Aiming at the above problems, we propose an intelligent computing offloading algorithm based on discrete SAC, which can adapt to the dynamic network environment and has the advantages of high stability and high sample utilization. The SACDTO strategy with the maximum entropy objective has a higher exploration ability to learn a continuous action space. * We extend the application scenario to multiple edge servers and study the computational offloading problem of various mobile users offloading tasks to multiple MEC servers through the base station. As multiple servers are deployed around mobile users, task offloading is no longer a simple binary offloading decision, and there are not only two processing methods: local execution or edge offloading. Instead, specific consideration should be given to whether task offloading should be performed and the number of the MEC server responsible for a task's execution after offloading. * We use the collaboration between the cloud, edge, and terminal to realize the training of a neural network with the massive computing power of cloud, and the trained scheduler can offload tasks to MEC servers for calculation. * We transform the original DAG into a series of embeddings that contain task profiles and dependency information for the application, which are transformed into inputs to the neural network.