# What are the policy-based methods?

The main goal of Reinforcement learning is to **find the optimal policy \\(\pi^{*}\\) that will maximize the expected cumulative reward**.
Because Reinforcement Learning is based on the *reward hypothesis*: **all goals can be described as the maximization of the expected cumulative reward.**

For instance, in a soccer game (where you're going to train the agents in two units), the goal is to win the game. We can describe this goal in reinforcement learning as
**maximizing the number of goals scored** (when the ball crosses the goal line) into your opponent's soccer goals. And **minimizing the number of goals in your soccer goals**.

## Value-based, Policy-based, and Actor-critic methods

In the first unit, we saw two methods to find (or, most of the time, approximate) this optimal policy \\(\pi^{*}\\).

- In *value-based methods*, we learn a value function.
  - The idea is that an optimal value function leads to an optimal policy \\(\pi^{*}\\).
  - Our objective is to **minimize the loss between the predicted and target value** to approximate the true action-value function.
  - We have a policy, but it's implicit since it **is generated directly from the value function**. For instance, in Q-Learning, we used an (epsilon-)greedy policy.

- On the other hand, in *policy-based methods*, we directly learn to approximate \\(\pi^{*}\\) without having to learn a value function.
  - The idea is **to parameterize the policy**. For instance, using a neural network \\(\pi_\theta\\), this policy will output a probability distribution over actions (stochastic policy).
  - 
  - Our objective then is **to maximize the performance of the parameterized policy using gradient ascent**.
  - To do that, we control the parameter \\(\theta\\) that will affect the distribution of actions over a state.

- Next time, we'll study the *actor-critic* method, which is a combination of value-based and policy-based methods.

Consequently, thanks to policy-based methods, we can directly optimize our policy \\(\pi_\theta\\) to output a probability distribution over actions \\(\pi_\theta(a|s)\\) that leads to the best cumulative return.
To do that, we define an objective function \\(J(\theta)\\), that is, the expected cumulative reward, and we **want to find the value \\(\theta\\) that maximizes this objective function**.

## The difference between policy-based and policy-gradient methods

Policy-gradient methods, what we're going to study in this unit, is a subclass of policy-based methods. In policy-based methods, the optimization is most of the time *on-policy* since for each update, we only use data (trajectories) collected **by our most recent version of** \\(\pi_\theta\\).

The difference between these two methods **lies on how we optimize the parameter** \\(\theta\\):

- In *policy-based methods*, we search directly for the optimal policy. We can optimize the parameter \\(\theta\\) **indirectly** by maximizing the local approximation of the objective function with techniques like hill climbing, simulated annealing, or evolution strategies.
- In *policy-gradient methods*, because it is a subclass of the policy-based methods, we search directly for the optimal policy. But we optimize the parameter \\(\theta\\) **directly** by performing the gradient ascent on the performance of the objective function \\(J(\theta)\\).

Before diving more into how policy-gradient methods work (the objective function, policy gradient theorem, gradient ascent, etc.), let's study the advantages and disadvantages of policy-based methods.

