# An Introduction to Q-Learning Part 2/2

## Unit 2, part 2 of the Deep Reinforcement Learning Class with Hugging Face 🤗

⚠️ A **new updated version of this article is available here** 👉 https://huggingface.co/deep-rl-course/unit1/introduction

*This article is part of the Deep Reinforcement Learning Class. A free course from beginner to expert. Check the syllabus here.*

⚠️ A **new updated version of this article is available here** 👉 https://huggingface.co/deep-rl-course/unit1/introduction

*This article is part of the Deep Reinforcement Learning Class. A free course from beginner to expert. Check the syllabus here.*

In the first part of this unit, **we learned about the value-based methods and the difference between Monte Carlo and Temporal Difference Learning**.

So, in the second part, we’ll **study Q-Learning**, **and implement our first RL agent from scratch**, a Q-Learning agent, and will train it in two environments:

- Frozen Lake v1 ❄️: where our agent will need to
**go from the starting state (S) to the goal state (G)**by walking only on frozen tiles (F) and avoiding holes (H). - An autonomous taxi 🚕: where the agent will need
**to learn to navigate**a city to**transport its passengers from point A to point B.**

This unit is fundamental if you want to be able to work on Deep Q-Learning (Unit 3).

So let’s get started! 🚀

##
**Introducing Q-Learning**

###
**What is Q-Learning?**

Q-Learning is an **off-policy value-based method that uses a TD approach to train its action-value function:**

*Off-policy*: we'll talk about that at the end of this chapter.*Value-based method*: finds the optimal policy indirectly by training a value or action-value function that will tell us**the value of each state or each state-action pair.***Uses a TD approach:***updates its action-value function at each step instead of at the end of the episode.**

**Q-Learning is the algorithm we use to train our Q-Function**, an **action-value function** that determines the value of being at a particular state and taking a specific action at that state.

The **Q comes from "the Quality" of that action at that state.**

Internally, our Q-function has **a Q-table, a table where each cell corresponds to a state-action value pair value.** Think of this Q-table as **the memory or cheat sheet of our Q-function.**

If we take this maze example:

The Q-Table is initialized. That's why all values are = 0. This table **contains, for each state, the four state-action values.**

Here we see that the **state-action value of the initial state and going up is 0:**

Therefore, Q-function contains a Q-table **that has the value of each-state action pair.** And given a state and action, **our Q-Function will search inside its Q-table to output the value.**

If we recap, *Q-Learning* **is the RL algorithm that:**

- Trains
*Q-Function*(an**action-value function**) which internally is a*Q-table***that contains all the state-action pair values.** - Given a state and action, our Q-Function
**will search into its Q-table the corresponding value.** - When the training is done,
**we have an optimal Q-function, which means we have optimal Q-Table.** - And if we
**have an optimal Q-function**, we**have an optimal policy**since we**know for each state what is the best action to take.**

But, in the beginning, **our Q-Table is useless since it gives arbitrary values for each state-action pair** (most of the time, we initialize the Q-Table to 0 values). But, as we'll **explore the environment and update our Q-Table, it will give us better and better approximations.**

So now that we understand what Q-Learning, Q-Function, and Q-Table are, **let's dive deeper into the Q-Learning algorithm**.

###
**The Q-Learning algorithm**

This is the Q-Learning pseudocode; let's study each part and **see how it works with a simple example before implementing it.** Don't be intimidated by it, it's simpler than it looks! We'll go over each step.

**Step 1: We initialize the Q-Table**

We need to initialize the Q-Table for each state-action pair. **Most of the time, we initialize with values of 0.**

**Step 2: Choose action using Epsilon Greedy Strategy**

Epsilon Greedy Strategy is a policy that handles the exploration/exploitation trade-off.

The idea is that we define epsilon ɛ = 1.0:

*With probability 1 — ɛ*: we do**exploitation**(aka our agent selects the action with the highest state-action pair value).- With probability ɛ:
**we do exploration**(trying random action).

At the beginning of the training, **the probability of doing exploration will be huge since ɛ is very high, so most of the time, we'll explore.** But as the training goes on, and consequently our **Q-Table gets better and better in its estimations, we progressively reduce the epsilon value** since we will need less and less exploration and more exploitation.

**Step 3: Perform action At, gets reward Rt+1 and next state St+1**

**Step 4: Update Q(St, At)**

Remember that in TD Learning, we update our policy or value function (depending on the RL method we choose) **after one step of the interaction.**

To produce our TD target, **we used the immediate reward $R_{t+1}$ plus the discounted value of the next state best state-action pair** (we call that bootstrap).

Therefore, our $Q(S_t, A_t)$ **update formula goes like this:**

It means that to update our $Q(S_t, A_t)$:

- We need $S_t, A_t, R_{t+1}, S_{t+1}$.
- To update our Q-value at a given state-action pair, we use the TD target.

How do we form the TD target?

- We obtain the reward after taking the action $R_{t+1}$.
- To get the
**best next-state-action pair value**, we use a greedy policy to select the next best action. Note that this is not an epsilon greedy policy, this will always take the action with the highest state-action value.

Then when the update of this Q-value is done. We start in a new_state and select our action **using our epsilon-greedy policy again.**

**It's why we say that this is an off-policy algorithm.**

###
**Off-policy vs On-policy**

The difference is subtle:

*Off-policy*: using**a different policy for acting and updating.**

For instance, with Q-Learning, the Epsilon greedy policy (acting policy), is different from the greedy policy that is **used to select the best next-state action value to update our Q-value (updating policy).**

Is different from the policy we use during the training part:

*On-policy:*using the**same policy for acting and updating.**

For instance, with Sarsa, another value-based algorithm, **the Epsilon-Greedy Policy selects the next_state-action pair, not a greedy policy.**

##
**A Q-Learning example**

To better understand Q-Learning, let's take a simple example:

- You're a mouse in this tiny maze. You always
**start at the same starting point.** - The goal is
**to eat the big pile of cheese at the bottom right-hand corner**and avoid the poison. After all, who doesn't like cheese? - The episode ends if we eat the poison,
**eat the big pile of cheese or if we spent more than five steps.** - The learning rate is 0.1
- The gamma (discount rate) is 0.99

**+0:**Going to a state with no cheese in it.**+1:**Going to a state with a small cheese in it.**+10:**Going to the state with the big pile of cheese.**-10:**Going to the state with the poison and thus die.**+0**If we spend more than five steps.

To train our agent to have an optimal policy (so a policy that goes right, right, down), **we will use the Q-Learning algorithm**.

**Step 1: We initialize the Q-Table**

So, for now, **our Q-Table is useless**; we need **to train our Q-function using the Q-Learning algorithm.**

Let's do it for 2 training timesteps:

Training timestep 1:

**Step 2: Choose action using Epsilon Greedy Strategy**

Because epsilon is big = 1.0, I take a random action, in this case, I go right.

**Step 3: Perform action At, gets Rt+1 and St+1**

By going right, I've got a small cheese, so $R_{t+1} = 1$, and I'm in a new state.

**Step 4: Update $Q(S_t, A_t)$**

We can now update $Q(S_t, A_t)$ using our formula.

Training timestep 2:

**Step 2: Choose action using Epsilon Greedy Strategy**

**I take a random action again, since epsilon is big 0.99** (since we decay it a little bit because as the training progress, we want less and less exploration).

I took action down. **Not a good action since it leads me to the poison.**

**Step 3: Perform action At, gets $R_{t+1}$ and St+1**

Because I go to the poison state, **I get $R_{t+1} = -10$, and I die.**

**Step 4: Update $Q(S_t, A_t)$**

Because we're dead, we start a new episode. But what we see here is that **with two explorations steps, my agent became smarter.**

As we continue exploring and exploiting the environment and updating Q-values using TD target, **Q-Table will give us better and better approximations. And thus, at the end of the training, we'll get an estimate of the optimal Q-Function.**

Now that we **studied the theory of Q-Learning**, let's **implement it from scratch**. A Q-Learning agent that we will train in two environments:

*Frozen-Lake-v1*❄️ (non-slippery version): where our agent will need to**go from the starting state (S) to the goal state (G)**by walking only on frozen tiles (F) and avoiding holes (H).*An autonomous taxi*🚕 will need**to learn to navigate**a city to**transport its passengers from point A to point B.**

Start the tutorial here 👉 https://colab.research.google.com/github/huggingface/deep-rl-class/blob/main/unit2/unit2.ipynb

The leaderboard 👉 https://huggingface.co/spaces/chrisjay/Deep-Reinforcement-Learning-Leaderboard

Congrats on finishing this chapter! There was a lot of information. And congrats on finishing the tutorials. You’ve just implemented your first RL agent from scratch and shared it on the Hub 🥳.

Implementing from scratch when you study a new architecture **is important to understand how it works.**

That’s **normal if you still feel confused** with all these elements. **This was the same for me and for all people who studied RL.**

Take time to really grasp the material before continuing.

And since the best way to learn and avoid the illusion of competence is **to test yourself**. We wrote a quiz to help you find where **you need to reinforce your study**.
Check your knowledge here 👉 https://github.com/huggingface/deep-rl-class/blob/main/unit2/quiz2.md

It’s essential to master these elements and having a solid foundations before entering the **fun part.**
Don't hesitate to modify the implementation, try ways to improve it and change environments, **the best way to learn is to try things on your own!**

We published additional readings in the syllabus if you want to go deeper 👉 https://github.com/huggingface/deep-rl-class/blob/main/unit2/README.md

In the next unit, we’re going to learn about Deep-Q-Learning.

And don't forget to share with your friends who want to learn 🤗 !

Finally, we want **to improve and update the course iteratively with your feedback**. If you have some, please fill this form 👉 https://forms.gle/3HgA7bEHwAmmLfwh9