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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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
Applicability of Policy Gradient Methods
Practical Implications of the Policy Gradient Simplification
Learn After
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
Applicability of Policy Gradient Methods
Practical Implications of the Policy Gradient Simplification
Related
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