# Research on High-Efficiency Routing Protocols for HWSNs Based on Deep Reinforcement Learning
## 3 Optimization Problem Analysis
### Algorithm Design
#### 3.3.2 Deep Reinforcement Learning  
Q-learning is a value iteration-based reinforcement learning algorithm that finds the optimal policy by continually updating the Q-values of state-action pairs. The original Q-learning algorithm is designed to handle finite and discrete action spaces. When faced with a vast number of state and action combinations, finding the action that maximizesthe Q-value becomes exceptionally challenging, as this requires operations that involve evaluating or maximizing over an infinite number of possible actions, which is impractical in real-world scenarios. The process of deep reinforcement learning is illustrated in Figure 3.  
The target network can improve the training stability of the DQN. Its main function is to select actions based on the maximum value of the current network \(Q(S,a)\) during DQN training, and then calculate the value \(y\) of the target network based on the maximum Q-value \(Q^{\prime}(Q^{\prime},a)\) of the next state \(S^{\prime}\). However, directly using the same current network for calculations can lead to unstable training. If the \(Q^{\prime}\) value changes too quickly, the \(y\) value will also increase accordingly. Therefore, an additional target network is used to calculate \(Q^{\prime}\) to ensure the stability of model training. The experience replay mechanism is employed to stabilize the training process. This involves using an experience buffer to store the states and actions the Agent acquires while interacting with the environment. During training, a random batch of samples is drawn from this buffer for learning. By storing all historical states and actions, this mechanism allows the information to be reused multiple times to optimize the DQN, thereby improving data efficiency. When calculating the target Q-value, the target network is used to calculate the maximum Q-value of the next state.  
\[y=r+\gamma\underset{a^{\prime}}{\text{max}}Q_{\text{target}}(s^{\prime},a^{ \prime}) \tag{16}\]  
where \(Q_{\text{target}}(s^{\prime},a^{\prime})\) is the Q-value of action \(a^{\prime}\) selected by the target network in the next state \(s^{\prime}\).  
The calculation equation for the loss function of the DQN algorithm is as follows:  
\[L(\theta)=\mathbb{E}\bigg{(}R+\gamma\underset{a^{\prime}}{\text{max}}Q(s^{ \prime},a^{\prime};\theta)-Q(s,a;\theta)\bigg{)}^{2} \tag{17}\]  
where the loss function defined in Equation (17) represents the difference between the target Q-value and the current Q-value. Once the loss function is obtained, the gradient descent method can be directly applied to optimize the weight parameters \(\theta\) of the convolutional neural network. In the DQN training process, to improve the efficiency and stability of learning, the DQN algorithm randomly samples pairs of states and actions from the historical dataset for training each time the Q-value is updated. Additionally, using two deep neural networks (DNNs) with the same structure but different parameters helps reduce the likelihood of oscillations and divergences during training, thereby enhancing the stability of the algorithm.  
Figure 3: Deep reinforcement learning process.