deep-rl-course/pr_676/en/unit2/q-learning-example.md

# A Q-Learning example [[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 take more than five steps.
- The learning rate is 0.1
- The discount rate (gamma) is 0.99

The reward function goes like this:

- **+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 dying.
- **+0** If we take 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: Initialize the Q-table [[step1]]

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 an action using the Epsilon Greedy Strategy [[step2]]

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

## Step 3: Perform action At, get Rt+1 and St+1 [[step3]]

By going right, I get a small cheese, so \\(R_{t+1} = 1\\) and I'm in a new state.

## Step 4: Update Q(St, At) [[step4]]

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

Training timestep 2:

## Step 2: Choose an action using the Epsilon Greedy Strategy [[step2-2]]

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

I took the action 'down'. **This is not a good action since it leads me to the poison.**

## Step 3: Perform action At, get Rt+1 and St+1 [[step3-3]]

Because I ate poison, **I get \\(R_{t+1} = -10\\), and I die.**

## Step 4: Update Q(St, At) [[step4-4]]

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 the TD target, the **Q-table will give us a better and better approximation. At the end of the training, we'll get an estimate of the optimal Q-function.**