Policy Gradient

The policy gradient method is a reinforcement learning algorithm that is used to find the optimal policy for a given system. The goal of the policy gradient method is to find a policy that maximizes the expected cumulative reward.

The policy gradient method is based on the idea of gradient ascent, which is a method for finding the maximum of a function by following the direction of the gradient. In the context of reinforcement learning, the policy is represented by a probability distribution over the actions, and the function to be maximized is the expected cumulative reward.

The policy gradient method updates the policy by following the gradient of the expected cumulative reward with respect to the policy parameters. The gradient is estimated using a technique called the likelihood ratio method, which involves taking the derivative of the expected cumulative reward with respect to the policy parameters and multiplying it by the ratio of the probability of the observed trajectory under the current policy and the probability of the same trajectory under a reference policy.

The policy gradient method can be used for both discrete and continuous action spaces, and it can be applied to both on-policy and off-policy learning. However, it can be sensitive to the choice of the reference policy and it can have difficulty with high-dimensional action spaces.

One of the variants of the policy gradient method is the REINFORCE algorithm, which is a simple and computationally efficient algorithm that estimates the gradient using a single sample of the trajectory. This algorithm has low variance but high bias.

Another variant is the Actor-Critic algorithm, which uses two neural networks, the actor network, and the critic network. The actor network is used to select actions, and the critic network is used to evaluate the actions. The actor network updates its parameters based on the gradients obtained from the critic network. This algorithm has low bias but high variance.

In summary, the policy gradient method is a reinforcement learning algorithm that is used to find the optimal policy for a given system by following the direction of the gradient of the expected cumulative reward. It can be used for both discrete and continuous action spaces and it can be applied to both on-policy and off-policy learning. However, it can be sensitive to the choice of the reference policy and it can have difficulty with high-dimensional action spaces. Variants of the policy gradient method include the REINFORCE algorithm and the Actor-Critic algorithm, which have their own advantages and disadvantages.