Let a rectangular grid to illustrate value functions for a simple finite MDP. The cells of the grid correspond to the states of the environment. At each cell, four actions are possible: north, south, east, and west, which deterministically cause the agent to move one cell in the respective direction on the grid. Actions that would take the agent off the grid leave its location unchanged, but also result in a reward of −1. Other actions result in a reward of 0, except those that move the agent out of the special states A and B. From state A, all four actions yield a reward of +10 and take the agent to A*. From state B, all actions yield a reward of +5 and take the agent to B*. A B B* A* Suppose the agent selects all four actions with equal probability in all states. The figure below shows the value function, vπ, for this policy, for the discounted reward case with γ = 0.9. Fill in the blank parts of the value function, using Bellman's equation. Use one decimal place accuracy. 3.3 8.8 4.4 5.3 1.5 1.5 3.0 1.5 0.5 0.1 0.7 0.7 0.4 -0.4 -1.0 -0.4 -0.6 -1.2 -1.9 -1.3 -1.2 -1.4 -2.0