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?
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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