Exercise 21.10 [10x10-exercise]
Compute the true utility function and the best linear approximation in $x$ and $y$ (as in Equation (4x3-linear-approx-equation)) for the following environments:
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A ${10}\times {10}$ world with a single $+1$ terminal state at (10,10).
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As in (a), but add a $-1$ terminal state at (10,1).
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As in (b), but add obstacles in 10 randomly selected squares.
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As in (b), but place a wall stretching from (5,2) to (5,9).
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As in (a), but with the terminal state at (5,5).
The actions are deterministic moves in the four directions. In each case, compare the results using three-dimensional plots. For each environment, propose additional features (besides $x$ and $y$) that would improve the approximation and show the results.
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