## 2 Related Work  
There is a lot of research on task offloading in MEC, which can be divided into three categories. First of all, for the dependent task offloading problem, some studies use the task call graph to model the complex dependencies between components in mobile applications [4; 5], and some also use DAG [6; 7; 8] to represent the relationships between tasks. Specifically, [PERSON] et al. [4] converts the task decision problem of cost minimization into the shortest path problem, and uses the classical Lagrangian relaxation-based aggregate cost algorithm to approximate the problem. [PERSON] et al. [5] combined a set of fine-grained tasks to form a common topology, which expanded the tasks into a general task map. [PERSON] et al. [6] proposed a graph mapping task offloading model based on Deep Reinforcement Learning (DRL), which converts DAG tasks into topological sequences according to custom priorities and then maps them into offloading decisions. [PERSON] et al. [7] proposed ACED, a multi-dependent task computing offloading algorithm based on DAG, which is an actor-critic mechanism with two embedded layers. [PERSON] et al. [8] proposed a reinforcement learning method based on a graph convolution network, which regards the task set as a directed acyclic graph and uses a graph convolution network to extract features from tasks. DRL is more suitable for online offloading in a fast fading channel environment. At present, convex relaxation methods [9] or heuristic local search methods [4,10] are mostly used for task offloading. However, both methods have their limitations and may fall into local optima. Moreover, it is impractical to re-solve the optimization problem once the external environment changes. DRL-based approaches include value-based and policy-based approaches. Frequently used value-based DRL methods include Deep Q Learning Network (DQN) [9], Double DQN [11], Dueling DQN [12], and Double Dueling DQN (D3 QN) [13]. However, when the number of wireless devices grows exponentially, DQN-based approaches are expensive. To solve this problem, some works have applied policy-based methods, such as the actor-critic method [14,15]. [PERSON] et al. [14] used the actor-critic model to solve the offloading problem of fine-grained tasks. In addition, the Proximal Policy Optimization (PPO) algorithm [16,17] has a good effect, and it can realize both discrete control and continuous control at the same time. However, PPO has the problem of sample inefficiency, which requires a huge amount of sampling to learn, which is unacceptable for practical application scenarios. Among them, [PERSON] et al. [16] studied the offloading problem in the multi-server and multi-user scenario, and [PERSON] et al. [17] used the PPO algorithm to make decisions on the dependent tasks' offloading. Some studies also use DDPG to solve the offloading problem [18,19]. Compared with PPO, this algorithm has higher sampling efficiency. As a deterministic strategy, DNN is used to directly construct the optimal mapping strategy from the input state to the output action. SAC uses a stochastic policy, which has advantages compared to the deterministic policy, as well as good stability and high sampling efficiency. Some recent research has been using SAC to solve the computational offloading problem. [PERSON] et al. [20] proposed centralized SAC offloading and decentralized SAC offloading algorithms. [PERSON] et al. [21] proposed a DAG task offloading method in MEC with inter-user cooperation and used a Quantified Soft Actor-Critic (QSAC) algorithm to solve the target problem. We summarize the pros and cons of these approaches in Table 1.  
Since the computing capacity of the cloud server is far greater than that of the MEC server, and it has enough resources to meet the peak demand of user requests [22], it can be considered that the cloud and MEC can cooperate to complete the offloading task. Some tasks with high computational complexity still need to be processed by the cloud server.