## 2 System Model and Problem Formulation
The global information of edge computing network is accessible to the control layer. Other heterogeneous edge computing nodes, as data layer nodes, are only responsible for data computing and transmitting and do not participate in any decision-making. When a task arrives, the control node divides the task into \(k\) subtasks according the data type contained in the task, where each subtask is completed independently by an edge computing node. To efficiently solve the above heterogeneous edge computing network resource scheduling problem, we introduced a multi-task alliance. In the considered network, the edge server acts as a control node to decompose tasks and build alliances for each task. The alliance is generated by the edge server with centralized decision-making, avoiding the complex broadcast process. Each edge computing node in the alliance undertakes at least one subtask and cooperates to complete the requirements of the task. After the task decomposition and allocation are completed, each edge computing node performs the sensing work for its subtask. Based on (1), we can obtain the computational energy consumption required to task m in the software-defined edge computing network as  
\[E_{m}^{comp}=\sum_{i=1}^{k}E_{p_{i},i}^{comp}=\sum_{i=1}^{k}e_{p_{i},i}^{comp}u _{p_{i},i}, \tag{4}\]  
Figure 1: Heterogeneous edge computing networks. where \(p_{i}\) is the edge computing node for subtask \(i\). Further, we can obtain the communication energy consumption required for the task \(m\) as  
\[E_{m}^{comm}=\sum\limits_{i=1}^{k}E_{p,i}^{comm}. \tag{5}\]  
Considering that the load balancing of edge computing network has great influence on network performance and network lifetime, we describe the resource scheduling of software-defined heterogeneous edge computing networks as a multi-objective optimization problem, which is expressed as  
\[\text{min}\left\{ \begin{array}{l}E^{totla}=\sum\limits_{m=1}^{M}\left(E_{m}^ {comp}+E_{m}^{comm}\right)\\ E^{balance}=\frac{\sum\limits_{m=1}^{M}p_{i}^{m}||E_{m}^{comp}+E_{m}^{comm}- \frac{E^{totla}}{P}||}{E^{totla}}\end{array} \right., \tag{6}\]  
where \(E^{balance}\) represents the load balancing degree of the network. The load balance here is a representation of the offset of the nodes in the network relative to the average energy consumption. We hope that the offset is as small as possible to achieve node load balancing. The total energy consumption takes into account the sum of the energy consumption of the computing node to process all subtasks and the communication energy consumption required for post-completion backhaul. The first constraint is the maximum load constraint of a single computing node, which takes into account the actual maximum computing power of the node. Further, we consider each sub-task allocation constraint as the second one, which requires each sub-task to be completed by a computing node alone. The above edge computing resource scheduling problem is a complex combinatorial optimization problem, which is usually difficult to be solved by traditional optimization methods. In the next section, we model the problem as an MDP process and study it based on deep reinforcement learning method.