Reinforced Learning (RL) refers to a class of problems where the goal is to learn (from experiences) what to do in different situations (or states of a system), so as to optimize a quantitative reward over time.

Mathematically, this can be translated into the identification of the function f(s,a), which gives for each state of the system s, the best action policy a, to maximize a reward r. The theoretical principles of this type of learning are the Markov decision processes and the optimal control theory.

Reinforced learning differs from other types of Machine Learning because the machine is not trained with an input dataset, instead it learns by trial and error. We often talk about an "agent" instead of a model, because the goal here is to learn how to choose actions over time.

In the absence of input data, the agent learns through experience to make choices. It is through the exploration of the states of a given environement and the available actions that the agent builds his learning examples ("this action was good", "this action was bad"), then, by trial and error, he identifies the policy that maximizes its long-term reward.

Figure 1 shows a typical learning scenario for reinforced learning in which An agent performs an action on the environment, this action is interpreted as a reward and a representation of the new state, and this new representation is passed to the agent.

Figure 1. Typical reinforcement scenario

Q-learning is probably the most used reinforced algorithm because of its simplicity. It is based on the learning of a function of the values ​​of the actions. This function represents "the expected utility for a given action, followed by an optimal policy". A policy is a set of rules that an agent follows to choose their actions based on states. The problem is thus composed of an agent, which can evolve in a set of states S, and which can choose in a set of actions A. The execution of an action in a state gives a reward r. The goal of the agent is to maximize his rewards. He must therefore identify what is the optimal action for each state, i.e. the one giving the greatest reward in the long run.

The Q-Learning algorithm therefore seeks to construct the Q-value function, (also called Q-table), which contains the maximum future rewards stretched for an action at each state. To illustrate this, let's take the example of a mouse (our agent) learning the shortest way out of a maze with 11 pieces as shown in Figure 2.

Figure 2. Maze

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