cart pole

Designing the Neural Network for DQN

Determining the layers and dimensions of each layer in a neural network for DQN is a crucial part of the design process. There's no one-size-fits-all answer, but here's a breakdown of the considerations and common practices:

1. Input and Output Layers are Determined by the Environment

Input Layer

The size of the input layer is directly determined by the state_size of your environment. In the CartPole example, state_size is 4, so your input layer must have 4 input units to accept the state representation.

Output Layer

The size of the output layer is determined by the action_size (number of possible actions) in your environment. For CartPole, action_size is 2 (move left or right), so your output layer needs 2 output units, each representing the Q-value for a corresponding action.

2. Hidden Layers - The Art of Approximation

Number of Hidden Layers

This is where experimentation comes in.

• Simple Problems (like CartPole): Often, 1-2 hidden layers are sufficient. CartPole is a relatively low-complexity problem, and a deeper network might not be necessary and could even lead to overfitting or slower training.
• Complex Problems: For more complex environments with high-dimensional state spaces or intricate dynamics, you might need deeper networks (3 or more hidden layers) to capture more abstract features and relationships in the data.

Dimension of Hidden Layers (Number of Units per Layer)

Rule of Thumb:

Start with dimensions that are somewhere between the input and output layer sizes, or similar to the input size. Powers of 2 (like 32, 64, 128, 256) are commonly used as layer sizes, but this is not a strict requirement.

Example in cart-pole.py:

The code uses two hidden layers, each with 64 units:

self.fc1 = nn.Linear(state_size, 64)
self.fc2 = nn.Linear(64, 64)

This is a reasonable starting point for CartPole.

Bottleneck vs. Wider Layers

• Bottleneck Architecture (decreasing layer sizes): You could try decreasing layer sizes (e.g., 128 -> 64 -> 32). This can sometimes help in feature extraction and reducing dimensionality but might also limit the network's capacity if done too aggressively.
• Wider Layers (constant or increasing layer sizes): Keeping layers at a similar size or even increasing them (e.g., 64 -> 64 or 64 -> 128) can provide more capacity for the network to learn complex functions.

3. Considerations for Network Design

• Complexity of the Environment: More complex environments generally require more complex networks (deeper and/or wider).
• Amount of Training Data: If you have a lot of training data, you can afford to train larger networks without overfitting. With limited data, simpler networks are often better.
• Computational Resources: Larger networks are more computationally expensive to train. Consider the resources available (CPU, GPU/MPS) when choosing network size.

Overfitting and Underfitting

• Overfitting (too complex): If your network is too complex for the problem, it might memorize the training data and perform poorly on unseen states (poor generalization).
  • Signs of overfitting: Very high performance on training data but poor performance in testing or simulation.
• Underfitting (too simple): If your network is too simple, it might not have enough capacity to learn the underlying Q-function effectively.
  • Signs of underfitting: Poor performance even on the training data.

4. Experimentation and Tuning

• Start Simple: Begin with a relatively simple network (e.g., 1-2 hidden layers with moderate dimensions like 32 or 64).
• Iterate and Evaluate: Train your DQN and evaluate its performance (e.g., average reward, success rate).
• Adjust Architecture: Based on the performance, you can:
  • Increase network size: Add more layers or increase the dimensions of existing layers if the agent is underperforming.
  • Decrease network size: Reduce layers or dimensions if you suspect overfitting or want to improve training speed.
  • Try different architectures: Experiment with different numbers of layers, layer types (e.g., convolutional layers for image-based inputs), and activation functions.

Hyperparameter Tuning

Network architecture is just one aspect. You'll also need to tune other hyperparameters like:

• Learning rate
• Discount factor (gamma)
• Epsilon decay
• Replay buffer size

These factors play a crucial role in optimizing performance.

Summary

Designing the neural network for DQN is an iterative process. Start with a reasonable architecture based on the problem complexity and input/output dimensions. Then, experiment, evaluate, and adjust the network architecture and hyperparameters to find the configuration that works best for your specific environment.

The architecture in cart-pole/cart-pole.py (2 hidden layers of 64 units) is a good starting point for CartPole and similar simple control tasks.

two models

Current Q-Values vs. Target Q-Values in DQN

In Deep Q-Networks (DQN), we estimate Q-values—which represent the expected cumulative reward for taking a certain action in a given state. However, to train the network effectively, we differentiate between current Q-values (predicted by the main model) and target Q-values (computed using the target network).

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1. Current Q-Values (self.model)

• These are predicted by the main Q-network (self.model) during training.
• The model takes the current state and outputs Q-values for all possible actions.
• The specific Q-value for the action taken is extracted for training.

In the replay() function in cart-pole.py:

current_q = self.model(states).gather(1, actions.unsqueeze(1)).squeeze(1)

• self.model(states): Predicts Q-values for all actions.
• .gather(1, actions.unsqueeze(1)): Extracts the Q-value corresponding to the action taken.
• .squeeze(1): Removes unnecessary dimensions.

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2. Target Q-Values (self.target_model)

• These represent a more stable learning target, helping prevent instability.

• The target Q-value is calculated using the Bellman equation:

  Q_{\text{target}}(s, a) = R + \gamma \max_{a'} Q_{\text{target}}(s', a')
  

• Instead of using the same network for both predicting and target computation, we use a separate target network (self.target_model).

• The Q-value for the next state (s') is taken from self.target_model and remains stable for some time.

In the replay() function in cart-pole.py:

next_q = self.target_model(next_states).detach().max(1)[0]
target = rewards + (1 - dones) * self.gamma * next_q

• self.target_model(next_states): Computes Q-values for all actions in the next state.
• .detach(): Prevents gradient updates (ensuring it's a stable target).
• .max(1)[0]: Selects the highest Q-value (best action) for the next state.
• target = rewards + (1 - dones) * self.gamma * next_q: Implements the Bellman update rule.

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Key Differences

Aspect	Current Q-Values (self.model)	Target Q-Values (self.target_model)
Purpose	Represents the learned Q-value estimates for each action in a given state.	Provides stable Q-values for training to reduce instability.
Where Computed	Extracted from the main Q-network (self.model).	Extracted from the target Q-network (self.target_model).
Usage in Training	Used to compute the predicted Q-value for the action taken.	Used as a stable target for updating the Q-values in the loss function.
Update Frequency	Updated in every training step.	Updated every 100 steps (or periodically).
Impact on Learning	Adapts quickly but can cause oscillations if used as a target.	Provides a stable reference point, reducing fluctuations and improving convergence.

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Why Use Target Q-Values?

If we used the same network (self.model) for both current and target Q-values, the target would be constantly changing as the model updates—causing instability. Using a separate target network (self.target_model) ensures that the target values change more gradually, leading to more stable training.

Here is the comparison table in Markdown syntax:

Comparison of self.model and self.target_model in Agent Class

Aspect	self.model	self.target_model
Purpose	Main Q-Network, learns from experience and updates via gradient descent.	Target Q-Network, provides stable Q-value estimates to prevent instability.
Where Used in Code	- agent.act(state): Used for selecting actions during exploration and exploitation. - self.model(states).gather(...): Used to compute the current Q-values during training. - self.optimizer.step(): Updated in every training step via backpropagation.	- self.target_model(next_states).detach().max(1)[0]: Used to compute target Q-values. - agent.update_target_model(): Synchronizes weights with self.model every 100 steps.
Update Frequency	Updated in every training step.	Updated every 100 steps (or periodically).
Impact on Training	Adapts quickly to new experiences, but if used for targets, can cause instability.	Provides stable target values, reducing oscillations and improving convergence.

This table clearly outlines the differences between self.model and self.target_model, their roles in the code, and how they contribute to the stability and learning process in DQN. Let me know if you need any modifications! 🚀

Full Code Comparison: Single vs. Two-Model DQN

Implementation	Code Snippet
Single Model (Unstable)

# Q-Value Prediction & Target Calculation (Unstable)
current_q = self.model(states).gather(1, actions.unsqueeze(1)).squeeze(1)
target_q = rewards + (1 - dones) * self.gamma * self.model(next_states).max(1)[0]

# Loss Calculation and Model Update
loss = F.mse_loss(current_q, target_q.detach())
self.optimizer.zero_grad()
loss.backward()
self.optimizer.step()

| Two Models (Stable DQN) |

# Q-Value Prediction (Stable DQN)
current_q = self.model(states).gather(1, actions.unsqueeze(1)).squeeze(1)

# Target Q-Value Calculation Using Target Model
next_q = self.target_model(next_states).detach().max(1)[0]
target_q = rewards + (1 - dones) * self.gamma * next_q

# Loss Calculation and Model Update
loss = F.mse_loss(current_q, target_q)
self.optimizer.zero_grad()
loss.backward()
self.optimizer.step()

# Target Model Synchronization (every 100 steps)
def update_target_model(self):
    self.target_model.load_state_dict(self.model.state_dict())