# A Learning Game-Based Approach to Task-Dependent Edge Resource Allocation
## 2 Related Work and Preliminary Technology  
### Related Work  
Existing research on the problem of task offloading and resource allocation falls into two main categories. The first assumes that ESs can provide resources at no cost [18; 19; 20; 21; 22; 23]. The other assumes that ESs provide resources under some form of incentive mechanism [24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. [PERSON] et al. [18] performed a joint optimization of channel allocation and dependent task offloading, as well as designed an algorithm based on genetic algorithms and deep deterministic policy gradients. [PERSON] et al. [19] studied the problem of optimal offloading and optimal allocation of computational resources under dependent task constraints and proposed a heuristic algorithm to solve the problem. [PERSON] et al. [20] optimized a task offload strategy, communication resources, and computing resources under the constraints of task processing delay and device energy consumption, and they went on to analyze the optimal solution from the perspectives of slow fading channels and fast fading channels. [PERSON] et al. [21] proposed an online framework for task offloading and resource allocation issues in edge computing environments. [PERSON] et al. [22] transformed the optimal resource allocation problem into an integer linear programming problem, and they proposed a distributed algorithm based on Markov approximation to achieve an approximately optimal solution within polynomial-time complexity. [PERSON] et al. [23] described the auxiliary caching-assisted computation offloading process, which is characterized as a problem of maximizing utility while considering the quality of experience (QoE). In addition, the problem was decomposed into two sub-problems for separate solutions. The aforementioned literature implicitly assumes that ESs can provide resources freely. However, in reality, ESs are driven by profit. Therefore, it is necessary to consider how to incentivize ESs. Based on whether the edge servers have sufficient resources, the study of incentive mechanisms can be divided into two aspects: First, when ESs lack adequate resources, the energy consumption of ESs acts as a counter incentive for users [24; 25]. Second, when the ESs have sufficient resources, the energy consumption of ESs becomes an incentive for users [26; 27; 28; 29]. [PERSON] et al. [24] studied the offloading problem involving multiple users and multiple edge nodes, where the energy consumption of the ESs was considered a constraining factor in finding the optimal solution. [PERSON] et al. [25]. investigated the task offloading and collaborative computing problem in mobile edge computing (MEC) networks, and they proposed a two-level incentive mechanism based on bargaining games. Additionally, to address the issue of edge node overload, the energy consumption of edge nodes was treated as a disincentive in the second stage of problem analysis. The aforementioned paper considered the possibility of ES overload, but its research problem and scenario differ from the context of this paper. The energy consumption of ESs serves as a positive incentive. [PERSON] et al. [26] studied resource allocation and pricing problems in an EC system, then formulated them as mixed-integer linear programming and proved the problem to be NP-hard. To solve this problem, auction-based mechanisms and linear programming-based approximation mechanisms were proposed and developed. [PERSON] et al. [27] studied the server resource pricing and task offloading problem by establishing a Stackelberg game model, as well as used a differential algorithm to solve for the optimal solution. [PERSON] et al. [28] aimed to increase the utilization rate of ESs' computing resources, and they formulated the optimization problem as a Stackelberg game. Supervised learning was designed to obtain equilibrium strategies. However, the Stackelberg games used in [27; 28] were based on a single variable and did not consider the dependencies between tasks. [PERSON] et al.