Advantage of Policy Gradients: Non-Differentiable Reward Functions
A significant advantage of the policy gradient method is that the cumulative reward function, R(τ), is not required to be differentiable. This is because the gradient is calculated with respect to the logarithm of the policy's probability, not the reward itself. This property allows for the application of any type of reward function in reinforcement learning, including those that are discontinuous or arbitrarily complex.
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Ch.4 Alignment - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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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
Learn After
In policy gradient methods, the gradient of the performance objective is estimated as an expectation over trajectories. Each trajectory's contribution to this estimate is the product of its cumulative reward and the gradient of its log-probability. Given this structure, why can these methods effectively handle tasks with non-differentiable reward functions, such as a simple binary reward for winning or losing a game?
Applicability of Policy Gradients with Discrete Rewards
For a policy gradient method to be applicable, the cumulative reward function must be differentiable, as its derivative is required when computing the gradient of the policy performance objective.