Policy Gradients Explained from Basics to Advanced Techniques

Policy gradients are a type of reinforcement learning algorithm that learns to take actions in an environment to maximize a reward.

The basic idea behind policy gradients is to update the policy directly by taking the gradient of the expected return with respect to the policy parameters.

In simple terms, policy gradients try to find the best action to take in a given situation by adjusting the policy parameters based on the reward received.

The policy gradient algorithm starts with an initial policy, which is typically a random policy, and then iteratively updates the policy parameters using the gradient of the expected return.

By using policy gradients, agents can learn to make decisions in complex environments where the reward signal is sparse or delayed.

The policy gradient is a fundamental concept in reinforcement learning, and it's essential to understand how it's derived. The policy gradient is the gradient of the policy performance with respect to the policy parameters.

To derive the policy gradient, we start with the probability of a trajectory given that actions come from the policy. This probability is given by the product of the probabilities of each action in the trajectory.

The log-derivative trick is a useful tool in deriving the policy gradient. It states that the derivative of the log of a function with respect to a parameter is equal to the derivative of the function with respect to the parameter multiplied by the function itself.

Using the log-derivative trick, we can derive the log-probability of a trajectory, which is simply the sum of the log-probabilities of each action in the trajectory.

The gradients of the environment functions are zero since the environment has no dependence on the policy parameters.

The gradient of the log-probability of a trajectory is thus the sum of the gradients of the log-probabilities of each action in the trajectory.

The policy gradient can be estimated using the sample mean of the gradients of the log-probabilities of each action in a set of trajectories.

Here's a summary of the key steps in deriving the policy gradient:

By following these steps, we can derive the policy gradient and use it to optimize the policy in reinforcement learning.

Policy Gradient Algorithms are a type of reinforcement learning algorithm that directly optimizes the policy, which is the mapping from states to actions. They are used to learn policies that maximize the expected cumulative reward.

One of the most popular policy gradient algorithms is REINFORCE, which uses an estimated return from an entire episode to update the policy parameter θ. This algorithm works by first initializing the actor π(S;θ) with random parameter values in θ, then generating the episode experience by following the actor policy π(S), and finally updating the actor parameters θ using the policy gradient theorem.

The policy gradient theorem states that the expected gradient of the log probability of an action is equal to the expected return of that action. This theorem is used to update the policy parameters θ to maximize the expected cumulative reward.

Another policy gradient algorithm is REINFORCE with Baseline, which adds a baseline to the estimated return to reduce the variance of the policy gradient. This algorithm initializes the actor π(S;θ) and critic V(S;ϕ) with random parameter values, then accumulates the gradients for the critic and actor networks using the policy gradient theorem and the baseline.

Policy gradient algorithms can be used to solve complex reinforcement learning problems, such as the CartPole-v1 and PixelCopter environments. They can also be used to learn policies that maximize the expected cumulative reward in a variety of domains, including robotics and finance.

Here is a list of the key components of policy gradient algorithms:

Note: The policy gradient theorem is a mathematical framework for updating the policy parameters, and it is a key component of policy gradient algorithms.

Policy optimization is a fundamental technique used in policy gradients to find the best policy parameters that maximize the objective function. This technique is heavily used in reinforcement learning, particularly in language model finetuning.

To implement policy optimization, we can use gradient ascent, which iterates over parameters using the update rule: θ = θ + α∇θJ(θ), where J(θ) is the objective function and α is the learning rate. The gradient of the objective function with respect to the current parameters is computed, multiplied by the learning rate, and then added to the parameters.

Gradient ascent is a widely used optimization algorithm in machine learning, and its variants are commonly used in training models. The update rule for gradient ascent involves three steps: computing the gradient of the objective function, multiplying it by the learning rate, and tweaking the parameters by addition or subtraction.

The REINFORCE algorithm is a popular implementation of policy optimization, which involves the following steps: initializing the actor with random parameter values, generating episode experiences by following the actor policy, calculating the return for each state in the episode sequence, accumulating the gradients for the actor network, and updating the actor parameters using the gradients.

Here's a summary of the REINFORCE algorithm steps:

By following these steps, we can implement policy optimization using the REINFORCE algorithm and find the best policy parameters that maximize the objective function.

A baseline is a function that can be added or subtracted from the policy gradient without changing its expected value. This allows for the reduction of variance in the sample estimate of the policy gradient, resulting in faster and more stable policy learning.

The most common choice of baseline is the on-policy value function, which characterizes the expected return for an agent starting in a given state and acting according to the current policy.

Using a baseline like the on-policy value function has the desirable effect of reducing variance in the sample estimate for the policy gradient. This results in faster and more stable policy learning.

The simplest method for learning a baseline is to minimize a mean-squared-error objective, which is done with one or more steps of gradient descent.

Here are some common variants of the policy gradient:

There are two more valid choices of weights that are important to know:

Policy optimization aims to learn a policy that maximizes the expected return over sampled trajectories.

We can use common gradient-based optimization algorithms like gradient ascent to learn this policy, but we need to compute the gradient of the expected return with respect to the current policy, also known as the policy gradient.

The most simple formulation of the policy gradient is the basic policy gradient, which can be computed by taking a sample mean over trajectories gathered from the environment by acting according to our current policy.

To generate an accurate estimate of the policy gradient, we need many trajectories, but several variants of the policy gradient can be derived to mitigate this problem.

One notable formulation of the policy gradient is the vanilla policy gradient, which requires a specialized technique like GAE to estimate the advantage function.

The return is assumed to be finite horizon, with a total number of steps T in the trajectory, and undiscounted, meaning no discount factor is applied to the rewards when computing the return.