Simplification of the Trajectory Log-Probability Gradient
After decomposing the trajectory log-probability gradient, it is typical in reinforcement learning settings to assume the environment's dynamics are not directly influenced by the policy parameters . Consequently, the derivative of the dynamics gradient, , is usually zero. We can therefore simplify the overall gradient to focus entirely on optimizing the policy component: This simplification allows for concentrating solely on policy updates without the need to understand or model the underlying environmental dynamics.
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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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Simplification of the Trajectory Log-Probability Gradient
In the derivation of a policy-based reinforcement learning algorithm, the gradient of the log-probability of a trajectory τ (a sequence of states and actions) with respect to policy parameters θ is transformed as shown below:
Initial form:
∂/∂θ log [ Π_t (π_θ(a_t|s_t) * P(s_{t+1}|s_t, a_t)) ]Decomposed form:
∂/∂θ Σ_t log π_θ(a_t|s_t) + ∂/∂θ Σ_t log P(s_{t+1}|s_t, a_t)By analyzing the components of the decomposed form, what is the most significant implication for the learning algorithm?
A key step in deriving policy-based reinforcement learning algorithms involves transforming the gradient of the log-probability of a trajectory. Arrange the following mathematical expressions to show the correct sequence of this transformation, starting from the initial combined form to the final decomposed form.
Evaluating a Policy Gradient Implementation
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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: What is the fundamental assumption that justifies simplifying this to just the policy component, ?
Applicability of Policy Gradient Methods
Practical Implications of the Policy Gradient Simplification