Policy Gradient Theorem

Advantage of Policy Gradients: Non-Differentiable Reward Functions

Decomposition of the Trajectory Log-Probability Gradient

Policy Gradient Objective with Advantage Function

Policy Gradient Estimate under Uniform Trajectory Probability

Score Function in Policy Gradients

During the derivation of the policy performance gradient, a key step transforms the expression Σ [∂Pr_θ(τ)/∂θ] R(τ) into a form that includes the term ∂log Pr_θ(τ)/∂θ. What is the primary analytical purpose of this transformation?

The following equations represent key steps in deriving the policy gradient. Arrange them in the correct logical order, starting from the initial gradient of the objective function to its final form as an expectation. Note: J(θ) is the objective function, Pr_θ(τ) is the probability of a trajectory τ under policy parameters θ, and R(τ) is the reward for that trajectory.

Analyzing a Flawed Policy Gradient Derivation

Policy Gradient Estimate under Uniform Trajectory Probability

In policy gradient methods, the gradient of the log-probability of a trajectory is initially expressed as the sum of two components: one related to the agent's actions and another related to the environment's transitions. The expression is then simplified by removing the environment's component before optimization. Given the initial expression: $\frac{\partial}{\partial \theta} \left[ \sum_{t=1}^{T} \log \pi_{\theta}(a_t|s_t) + \sum_{t=1}^{T} \log \text{Pr}(s_{t+1}|s_t, a_t) \right]$ What is the fundamental assumption that justifies simplifying this to just the policy component, $\frac{\partial}{\partial \theta} \sum_{t=1}^{T} \log \pi_{\theta}(a_t|s_t)$?

Applicability of Policy Gradient Methods

Practical Implications of the Policy Gradient Simplification