<|im_start|>system
You are a helpful AI assistant.<|im_end|>
<|im_start|>user
Can you write the following in a better way? After that, can you point out some mistakes, if there are any? 

In policy gradient methods the agent is composed of two components, an actor and a critic. The actor represents the policy and is usually implemented by a with a neural network. The actor takes as input the agent's observation and outputs a probability distribution over the action space. The critic estimates the value function of the state and usually has the same neural network architecture as the actor but outputs one real value, corresponding the value of the state.<|im_end|>
<|im_start|>assistant
In policy gradient methods, the agent consists of two components: an actor and a critic. The actor represents the policy and is typically implemented using a neural network. It takes the agent’s observation as input and outputs a probability distribution over the action space. The critic estimates the value function of the state and usually has the same neural network architecture as the actor. However, it outputs a single real value that corresponds to the value of the state.

One mistake in the original text is that it says “implemented by a with a neural network” instead of “implemented using a neural network”.<|im_end|>
<|im_start|>user
And who is the actor responsible to, if anyone and the same for the critic?<|im_end|>
<|im_start|>assistant
Based on what you have written, the actor is responsible for representing the policy and the critic is responsible for estimating the value function of the state.  Since you asked who they would be responsible to, the actor would would be responsible to whoever manages the policy and the critic would would be responsible to whoever manages the state.  However, I believe you may be suggesting the agent is who the actor is responsible to as the actor takes the agent's observation as input.<|im_end|>
<|im_start|>user
Reformat for clarity<|im_end|>
<|im_start|>assistant
Here's the reformatted text with paragraph breaks. 

>When employing an actor-critic policy-gradient reinforcement learning method, the algorithm learns two components, an actor and a critic function.
>
>For problems with non-trivial action and observation spaces, the actor and critic functions are usually represented by deep neural networks. The actor network maps each possible observation in the agent's observation space to a probability distribution over possible actions in the action space. The critic network maps each possible observation to a corresponding expected value estimate.
>
>In practice, some of the early layers are often shared between the actor and critic networks, though this is not required. This is based on the intuition that some of the same processing will need to be done by both the actor and the critic network, though they are trained to produce different outputs.
>
>An example of this is that if working with a pixel-valued observation space, both the actor and critic networks will need to learn edge-detection.<|im_end|>