## 2 Related Work  
The path selection problem stems from the basic trade off between the cost of service migration (transmission cost and migration cost) and the improvement of users' expectation on QoS that can be achieved after migration. Recently, extensive efforts are paid to enforcing QoS guarantees and fault tolerance in edge service migrations [27]. For instance, [PERSON] et al. [28] proposed a layered migration framework that divided the base package into three layers: base layer, application layer, and instance layer. A copy of the base layer is stored on each ES, so it is unnecessary to transfer it on every migration. The application layer contains the basic data information required for service operation. The running state of the service is placed in the instance layer. When migrating a service, the application layer is first migrated, then the service is suspended, and the instance layer is transferred to the target ES. Finally, the base layer, application layer, and instance layer are combined in the target ES to reconstruct the running service. [PERSON] et al. [29] performed delta encoding, deduplication, and data compression operations in sequence before service data migration to reduce the amount of data that needs to be transmitted, thereby improving the efficiency of service migration. However, the data will be distorted to a certain extent after being compressed, and the compression time of the data will also affect the QoS of service migration. [PERSON] et al. [30] proposed an optimization method for user overhead and provider operating costs in a large-scale edge computing environment. Firstly, the network and user movement space are modeled. Then, random global search schemes such as simulated annealing, tabu search, greedy algorithm, and binary search are combined to search for the best path for migration, thereby reducing data migration overhead and saving costs. [PERSON] et al. [31] proposed a collaborative edge caching scheme to jointly optimize task placement and migration in vehicle edge computing. This scheme formulates the joint optimization problem as a dual-time-scale Markov Decision Process (MDP) according to the relationship between the task migration time scale and the vehicle movement time scale, which minimizes the task migration cost while satisfying the task migration delay constraint. However, when the MDP state space is large, the cost function and transition probability of MDP may change with time, and the processing capacity of ES is limited, and the resulting problems become difficult to solve. [PERSON] et al. [32] approximate the underlying state space by the distance between users and service locations, which is much faster than traditional methods based on standard value or policy iteration and can efficiently compute service migration policies for 2D mobility models. Representing task migration as an online multidimensional integer linear programming problem, [PERSON] et al. [33] proposed a decentralized reactive method that generates online migration decisions by employing a dynamic learning mechanism. Different from [33], [PERSON] et al. [34] first relax the binary constraints of the transfer decision, and transform the problem into a series of convex problems that can be optimally solved. Then, a rounding method for binary decision solution recovery based on the nature of the problem is proposed to maximize the weighted unloading rate for all users while minimizing the migration cost as much as possible. In recent years, with the rise of the third wave of artificial intelligence technology, many researchers have begun to combine Reinforcement Learning (RL) technology to deal with the problem of service migration. [PERSON] et al. [35] designed a reinforcement learning-based framework for a single-user edge computing service migration system, which first assumed that the user's moving trajectory was fixed and known, and then used RL methods to find the optimal communication path between two edge servers for service migration.