Reinforcement Learning

$15$ points

Consider the non$-$deterministic reinforcement environment drawn below. States are represented by circles, and actions by squares. The Probability of a transitions is indicated on the arc from actions to states. Immediate rewards are indicated above and below states. Once the agent reaches the end state the current episode ends.

$13.(15$ points$)$ Consider two possible policies: always take action $x$ or always take action $Y.$ For each policy, compute the answers to the following questions.

$($a$)$ What paths could be taken?

$($b$)$ What is each path's probability?

$($c$)$ What is each path's reward?

$($d$)$ What is the utility of each state?