๐ Understanding Reinforcement Learning (RL)
Reinforcement Learning is a machine learning paradigm where an agent learns to make decisions by interacting with an environment. Instead of being told what the correct action is (as in supervised learning), the agent learns by trial and error, receiving:
State (s): the current situation
Action (a): what the agent chooses to do
Reward (r): feedback signal after taking an action
Next state (s′): the state the agent transitions into
The agent’s goal is to learn a policy—a rule for choosing actions—that maximizes cumulative long-term reward.
๐ What Is Q-Learning?
Q-Learning is a fundamental model-free RL algorithm.
Model-free means: it doesn’t need to know the environment’s dynamics (transition probabilities, rules, etc.). It just learns from experience.
It learns a function:
๐ Q(s, a)
The quality of taking action a in state s, i.e., how good that action is in the long run.
Once learned, the agent uses Q-values to choose actions:
Pick the action with the highest Q(s, a) → greedy exploitation
Sometimes explore other actions → exploration (e.g., ฮต-greedy)
๐ง The Q-Learning Update Rule
After performing action a in state s, receiving reward r, and landing in state s′, Q-learning updates its estimate as:
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Q(s,a)←Q(s,a)+ฮฑ[r+ฮณ
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Where:
ฮฑ (alpha) = learning rate
ฮณ (gamma) = discount factor (importance of future rewards)
r = immediate reward
max Q(s′, a′) = best estimated future value from the next state
✔ What this update means:
Move Q(s, a) slightly toward a better estimate of its long-term value.
The term
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is the target—what we think the true value should be.
๐ฏ Why Is Q-Learning Powerful?
✓ Off-policy
It learns the value of the optimal policy regardless of how the agent behaves (exploration policy).
✓ Converges to optimal solution
With proper learning rate decay and exploration, it provably converges to the optimal Q-values.
✓ Simple and effective
Works well in small, discrete environments (e.g., Gridworld, Frozen Lake).
๐ Limitations of Q-Learning
Works only with discrete states and actions, unless approximations (like neural networks) are used.
Can be slow to converge in large environments.
Requires storing a Q-table of size |states| × |actions| → not scalable for big problems.
๐ค Beyond Q-Learning: Deep Q-Networks (DQN)
To handle large or continuous state spaces, we replace the Q-table with a neural network.
This leads to DQN, which famously learned to play Atari games from raw pixels.
๐งฉ Simple Example
Imagine a robot in a 3×3 grid trying to reach a goal cell.
Each move: −1 reward
Reaching goal: +10 reward
Q-Learning will update Q-values based on experiences until it finds the shortest path to the goal.
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