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Numerical Input 1 . 0 / 1 . 0 point ( graded ) Assume the agent uses REINFORCE for learning a policy while navigating in

Numerical Input
1.0/1.0 point (graded)
Assume the agent uses REINFORCE for learning a policy while navigating in a continuous 2D square maze, with center at origin. It starts at the state . The agent's policy is parameterized by a linear function where the final layer outputs the mean action . Here, is a 2x2 matrix initialized as all zeros, and is the state. During execution, the agent then samples an action , a 2-dimensional Gaussian distribution with mean and identity variance. The first trajectory is: . The trajectory ends in because the agent falls into a trap and receives a negative reward of (. Otherwise, the agent receives a reward of for every previous step. Assume .
What is the return at state ? Please specify to the 4th decimal place.

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