Update qLearning.md

docs/machine-learning/qLearning.md

@@ -1,16 +1,16 @@
 ---
-
-id: q-learning  
-title: Q-Learning Algorithm  
-sidebar_label: Q-Learning  
-description: "An overview of the Q-Learning Algorithm, a model-free reinforcement learning method that learns the optimal action-value function to guide decision-making."  
-tags: [machine learning, reinforcement learning, q-learning, algorithms, model-free]  
-
+id: q-learning
+title: Q Learning Algorithm
+sidebar_label: Q Learning
+description: "An overview of the Q-Learning Algorithm, a model-free reinforcement learning method that learns the optimal action-value function to guide decision-making."
+tags: [machine learning, reinforcement learning, q-learning, algorithms, model-free]
 ---
 
 ### Definition:
 The **Q-Learning Algorithm** is a model-free reinforcement learning algorithm used to find the optimal action-selection policy for any given finite Markov Decision Process (MDP). It works by learning the value of actions in specific states without needing a model of the environment and aims to optimize long-term rewards.
 
+<Ads />
+
 ### Characteristics:
 - **Model-Free**:  
   Q-Learning does not require prior knowledge of the environment's dynamics and learns directly from experience.
@@ -24,16 +24,16 @@ The **Q-Learning Algorithm** is a model-free reinforcement learning algorithm us
 ### How It Works:
 Q-Learning learns an **action-value function (Q-function)** that maps state-action pairs to their expected cumulative rewards. The Q-value is updated using the following equation:
 
-\[
+$$
 Q(s, a) \leftarrow Q(s, a) + \alpha \left[ r + \gamma \max_{a'} Q(s', a') - Q(s, a) \right]
-\]
+$$
 
-- **\( s \)**: Current state
-- **\( a \)**: Action taken in the current state
-- **\( r \)**: Reward received after taking action \( a \)
-- **\( s' \)**: Next state after taking action \( a \)
-- **\( \alpha \)**: Learning rate (controls how much new information overrides old)
-- **\( \gamma \)**: Discount factor (determines the importance of future rewards)
+- $ s $: Current state
+- $ a $: Action taken in the current state
+- $ r $: Reward received after taking action $ a $
+- $ s' $: Next state after taking action $ a $
+- $\alpha $: Learning rate (controls how much new information overrides old)
+- $ \gamma $: Discount factor (determines the importance of future rewards)
 
 ### Steps Involved:
 1. **Initialization**:  
@@ -51,6 +51,8 @@ Q(s, a) \leftarrow Q(s, a) + \alpha \left[ r + \gamma \max_{a'} Q(s', a') - Q(s,
 5. **Repeat**:  
    Continue until the learning converges or a stopping condition is met.
 
+<Ads />
+
 ### Problem Statement:
 Given an environment defined by states and actions with unknown dynamics, the goal is to learn the optimal Q-function that allows an agent to make decisions maximizing cumulative rewards over time.
 
@@ -59,10 +61,10 @@ Given an environment defined by states and actions with unknown dynamics, the go
   A matrix where each row represents a state, and each column represents an action. The values represent the learned Q-values for state-action pairs.
 
 - **Epsilon-Greedy Strategy**:  
-  A common method to balance exploration and exploitation. The agent selects a random action with probability \( \epsilon \) and the best-known action with probability \( 1 - \epsilon \).
+  A common method to balance exploration and exploitation. The agent selects a random action with probability $ \epsilon $ and the best-known action with probability $ 1 - \epsilon $.
 
 - **Convergence**:  
-  Q-Learning converges to the optimal Q-function given an infinite number of episodes and a decaying learning rate.
+  Q-learning converges to the optimal Q-function given an infinite number of episodes and a decaying learning rate.
 
 ### Example:
 Consider a grid-world environment where an agent navigates to collect rewards:
@@ -73,9 +75,10 @@ Consider a grid-world environment where an agent navigates to collect rewards:
 
 **Update Step**:
 After moving from (1,1) to (1,2) with action "Right" and receiving a reward of 0:
-\[
+
+$$
 Q(1,1, \text{Right}) \leftarrow Q(1,1, \text{Right}) + \alpha \left[ 0 + \gamma \max_{a'} Q(1,2, a') - Q(1,1, \text{Right}) \right]
-\]
+$$
 
 ### Python Implementation:
 Here is a basic implementation of Q-Learning in Python:
@@ -123,6 +126,4 @@ print("Training completed.")
 ```
 
 ### Conclusion:
-Q-Learning is a powerful and foundational reinforcement learning technique that enables agents to learn optimal policies through direct interaction with an environment. Its simplicity and effectiveness make it a popular choice for many RL applications.
-
----
+Q-learning is a powerful and foundational reinforcement learning technique that enables agents to learn optimal policies through direct interaction with an environment. Its simplicity and effectiveness make it a popular choice for many RL applications.