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The policy gradient, which represents the gradient of the objective function $$J(	heta)$$, can be reformulated to use the advantage function $$A(s_t, a_t)$$. This substitution is a common technique in policy gradient algorithms because it helps to reduce the high variance often associated with gradient estimates, leading to more stable and efficient learning.

Policy Gradient Reformulation using Advantage Function

An agent is being trained using a policy gradient method to navigate a maze where the final reward can vary significantly due to random bonus items. For example, two identical paths taken by the agent might result in total rewards of +10 and +100, respectively. The learning process is observed to be very unstable; the agent's performance fluctuates wildly between training iterations. The current policy update rule for an action `a_t` taken in state `s_t` is proportional to `log π(a_t|s_t) * G_t`, where `G_t` is the total reward from time step `t` onward. Analyze the likely cause of the learning instability described in this scenario. Then, propose a specific modification to the term that multiplies `log π(a_t|s_t)` in the update rule to mitigate this issue, and justify why your proposed modification would lead to more stable learning.

Stabilizing Policy Gradient Learning in a High-Variance Environment

In the context of policy gradient methods, explain the primary rationale for using the advantage function to weight the policy gradient term, rather than using the total cumulative reward. How does this reformulation typically affect the stability of the training process?

Rationale for Using the Advantage Function

A reinforcement learning agent is being trained using a policy gradient method. During training, the agent's performance is highly erratic, and the estimated gradients for policy updates have very high variance. Which of the following changes to the gradient estimation process is most directly aimed at stabilizing learning by reducing this variance?

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