What is policy gradient?

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Policy Gradient is a family of reinforcement learning (RL) algorithms that directly optimize an agent’s policy, which is the mapping from states to actions, instead of learning the value function like in Q-learning. It’s widely used in continuous action spaces or when the policy needs to be stochastic.

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🔹 Key Concepts:

1. Policy ($\pi_\theta$)

   • A policy defines the agent’s behavior.

   • In policy gradient methods, the policy is parameterized by $\theta$ (weights of a neural network, for example).

2. Objective

   • The goal is to maximize the expected cumulative reward:

     $$J(\theta) = \mathbb{E}_\pi [R]$$

   • Policy gradient algorithms compute the gradient of this objective with respect to $\theta$ and update the policy using gradient ascent.

3. Stochastic Policies

   • Policy gradient naturally handles stochastic policies, where actions are chosen probabilistically.

   • Example: $\pi_\theta(a|s)$ gives the probability of taking action $a$ in state $s$.

4. Update Rule

   • Parameters are updated in the direction of higher expected reward:

     $$\theta \leftarrow \theta + \alpha \nabla_\theta J(\theta)$$

   • Techniques like REINFORCE or Actor-Critic are commonly used to compute $\nabla_\theta J(\theta)$.

5. Advantages

   • Works well in continuous or high-dimensional action spaces.

   • Can learn stochastic policies, allowing exploration naturally.

6. Challenges

   • High variance in gradient estimates.

   • Often slower to converge than value-based methods.

   • Requires careful tuning of learning rate and reward normalization.

✅ In short:

Policy gradient methods directly learn the policy by optimizing the expected reward using gradient ascent. They are ideal for environments with continuous actions or where stochastic policies are required, forming the foundation of advanced RL algorithms like Actor-Critic, PPO, and TRPO.

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