❓ Question

The evidence is clear: the `argmax` operation from Q-learning is unusable in a continuous action space. Our only path forward is to design a new kind of "brain" for our agent—a **policy network**—that can learn to handle this complexity. Before we write any PyTorch code, we must first be the architect. A neural network is a function approximator; we need to be precise about what function we are trying to approximate. Let's design our policy network by answering the following questions. 1. **The Input:** What information does the policy need to make a decision? Based on this, what should the **input size** (number of input neurons) of our network be? 2. **The Policy Type:** Should our agent's policy be **deterministic** (always choosing the exact same action for a given state) or **stochastic** (choosing actions from a probability distribution)? For exploration and for the REINFORCE algorithm, which type is necessary? 3. **The Output:** To handle a continuous action space, our stochastic policy will be modeled as a **Gaussian (Normal) probability distribution**. - What, therefore, should our neural network output? - How many output neurons will our network need to define this distribution for `MountainCarContinuous-v0? 4. **The Architecture:** The number and size of the hidden layers are design choices. For a simple problem like `MountainCarContinuous-v0`, we don't need a massive network. How many layers should it have? What would be a reasonable number of neurons for these layers (e.g., 64, 128, 256)?

Click here to review the architectural blueprint

**Detective's Blueprint:** 1. **Input Size:** The network's input must be the state. The `MountainCarContinuous-v0` observation space has a shape of `(3,)`, so our network needs **3 input neurons**. 2. **Policy Type:** REINFORCE is a stochastic policy gradient algorithm. It requires a **stochastic** policy to explore and to calculate log-probabilities. 3. **Output Size:** A Gaussian distribution is fully defined by two parameters: its **mean ($\mu$)** and its **standard deviation ($\sigma$)**. To define a 1D Gaussian distribution, the network must output both the mean and the standard deviation. Therefore, it needs **2 output neurons**. One will represent $\mu(s)$, and the other will represent $\sigma(s)$. 4. **Architecture:** A simple architecture like two hidden layers with **128 neurons each** is a robust and common starting point for this kind of problem. We now have a complete blueprint for our agent's brain. In the next step, we will use PyTorch's `nn.Module` to build it.