Exercise 17.7 [threshold-cost-exercise]

For the environment shown in Figure sequential-decision-world-figure, find all the threshold values for $R(s)$ such that the optimal policy changes when the threshold is crossed. You will need a way to calculate the optimal policy and its value for fixed $R(s)$. (Hint: Prove that the value of any fixed policy varies linearly with $R(s)$.)

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