# Reinforcement Learning (1): Q-Learning basics

Hi! In the following posts, I will introduce Q-Learning, the first part to learn if you want to pick up reinforcement learning. But before that, let us shed light on some fundamental concepts in reinforcement learning (RL).

## Kindergarten Example

Q-Learning works in this way: do an action and get reward and observation from the environment, as shown below. Image is taken from here :

Berkeley’s CS 294: Deep Reinforcement Learning by John Schulman & Pieter Abbeel

Imagine a baby boy in a kindergarten and how he performs on the first day. He does not know the kindergarten and knows nothing about how to behave. So he begins with random actions, say he hits the other kids, and when he performed this, he has no idea if it is right or not. Then the teacher becomes mad and gives him a punishment (a negative reward), then he knows hits others is not a good action; in the next time, the boy washes his lunch box, and the teacher rewards him with candy, then he knows this action is a good one. So in our kindergarten example, simply the Agent is the boy, who has no knowledge in the very beginning; Action is how he behaves; Environment contains all the objectives that he could perform on; Reward is something he gets from the environment (punishment or the candy), and Observation is what he could observe or the feedback from the environment.

Candies lol

## Exploitation vs. Exploration

To understand how Q-learning works, it is important to know exploration and exploitation.
Let’s say our baby boy from the kindergarten goes home one day, and his mom prepares five boxes (we call them A-E), where there are different numbers of candies inside the boxes and he doesn’t know which one has more candies. So if his goal is to get as much candy as possible, what he would do?

Method 1: Obviously he could choose an arbitrary box each time. However, it is not guaranteed that he could get as much as possible.

Method 2: Another method would choose a “possible” box. Each time, he can choose the box with the maximum expectation of the candies. So to get a distribution of the candies, say he could open box 1000 times uniformly then keep track of the number of candies.

Method 3: If he has some prior knowledge about these boxes, for example, his mom told him that box A has 10 (expectation), box B has 20 (expectation) and others unknown. So based on his goal, it seems box B is a good choice. But box C might have even more candies! We could either choose box B, or randomly choose a box from C-E.

We call these methods policies in Q-learning. In brief, we choose our action (choose a box) based on our current state in a policy. So we define latex]\pi[/latex] as a policy, which maps states to actions.

Exploitation is to choose an action based on information that we have known. Method 2 is an exploitation-only policy. We say we know the expectations of all actions and then choose the best one.
Exploration is to explore the new actions that we have no information about. Method 1 is an exploration-only policy. Method 3 is a balanced version of these two. This provides us the idea of $\epsilon$-greedy policy.

## Epsilon-greedy policy

Ranges from 0 to 1,$\epsilon$ is the probability of exploration, which is set to search for new things. Typically, we just random a state and return that action. In practice, we initialize it with a value between 0 and 1; then we usually let it shrink during episodes $t$ . An Episode is a whole game process from the start to the terminal state. Say in Flappy Bird, you start the game until the death state. Intuitively, imagine when an agent starts to play a new game, it has no “experience” about the game, so it is natural to go randomly; after some episodes, it is about to learn the skills and tricks, then it tends to use its own experience to play instead of randomly choose an action, because the more episodes it plays, the more confident it is about the experience (the more accurate the reward approximation is). There are various settings to $\epsilon$, say $\epsilon=\frac{1}{ \sqrt { t } }$, where $t$ refers to episode.

Slide from Percy Liang

## Q-table

Q-learning has a table called Q-table, which is a table of states, actions and approximated rewards. Let’s get back to the kindergarten example.

Kindergarten states and actions

We simplify the problem: states for the boy are washing lunch box (wash) and hitting others (hit), there are four actions marked as action A to D. Our Q table shows bellow, where we could observe that each row is a state and the corresponding reward values to different actions. Some state-action pairs are illegal and reach no values. The values indicate number of candies as rewards.

A B C D
Wash 10 -5
Hit -10 5

Q-table example