Q $[6$ points$]$ Consider the following Q$-$matrix where we have $6$ states: A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ Compute $Q(B,E)$ Using the $Q-$learning algorithm with $=0\mathrm{.}5$ and $=0\mathrm{.}8.$ The reward is $-2$ for all states except $F$ where the reward is $100.$

Use one of the following formulas

$Q(S,a)larr(1-)Q(S,a)+(r+**ma{x}_{a^{\text{'}}}(Q(S^{\text{'}},a^{\text{'}})))$

$Q(S,a)larrQ(S,a)+(r+**ma{x}_{a^{\text{'}}}(Q(S^{\text{'}},a^{\text{'}}))-Q(S,a))$

Answer:

Q$2)[6$ points$]$ Assuming the use of a single simple perceptron. The output $=1$ if ${\displaystyle \underset{i}{\overset{?}{}}}{w}_i{x}_i+b_{i}0.$ Clearly show the used weights and threshold that detect the decision boundary below the given line $($i$.$e$.,$ output $=1$ for area under the line$).$