15. Why Do We Create Two Networks (Local and Target) in Deep Q-Learning?

In Deep Q-Learning (DQL), two neural networks—Local (Online) Network and Target Network—are used to address instability and improve the training process. Here's a detailed explanation of why they are needed:

1. The Problem: Instability in Q-Learning

In Q-Learning, the goal is to iteratively update the Q-values (state-action value estimates) to approximate the Bellman equation:

Q(s, a) = r + γ max_a' Q(s', a')

When a neural network is used to estimate the Q-values:

Continuous updates: The network’s weights change frequently, making the target values (r + γ max Q(s', a')) highly volatile.
Feedback loop: The same network is used for both predicting Q-values and generating target Q-values, causing the model to "chase its own tail" and leading to divergence or oscillations in learning.

2. The Solution: Two Networks

To stabilize training, DQL introduces two networks:

Local (Online) Network: This network is updated every training step. It generates predictions (current Q-values) for actions based on the current weights.
Target Network: This network is a delayed copy of the local network and generates the target Q-values for the Bellman equation. It is updated less frequently.

3. Why Two Networks?

a. Stabilize Target Values

The target network holds the parameters fixed for several training steps, preventing rapid changes in target values. This reduces the risk of feedback loops where the network chases constantly shifting targets.

b. Break Correlation

The local network's predictions are used to determine the best action, while the target network provides a stable target value. This separation helps break correlations that can arise when a single network serves both purposes.

c. Improved Convergence

By keeping the target network static for a while, the updates to the local network focus on improving predictions based on stable targets. Periodically updating the target network ensures that the target values evolve as the local network learns, balancing stability and adaptability.

4. How It Works in Practice

The local network is updated at every step during training using backpropagation. The target network is updated periodically:

Hard Update: Copy all weights from the local network to the target network after N steps:
```
θ_target ← θ_local
```
Soft Update: Gradually update target network weights using a factor τ (e.g., 0.01):
```
θ_target ← τ · θ_local + (1 - τ) · θ_target
```

5. Benefits

Stable Learning: Reduces the instability caused by rapidly changing target values.
Better Approximation: Allows the network to converge more reliably to optimal Q-values.
Improved Performance: Helps achieve higher performance in environments with complex state-action spaces.

Summary

Two networks are used in Deep Q-Learning to stabilize training and improve performance:

The Local Network generates predictions and is updated frequently.
The Target Network provides stable target Q-values and is updated periodically.

This separation ensures the model learns effectively while avoiding divergence caused by rapidly shifting targets.