$(13)$ In this grid world $(30$ points$)$

The agent starts at position $S($top$-$left corner$).$

The goal is located at position $G($bottom$-$left corner$).$

There is one obstacle located at position $x($center$).$

The agent can move up$,$ down, left, or right within the grid, but cannot move into the

obstacle cell.

The objective for the agent is to navigate from the start position $S$ to the goal position $G$ while

avoiding the obstacle $x.$ The agent receives a reward of $+10$ for reaching the goal and a penalty

of $-10$ for hitting the obstacle. All other movements incur a small penalty of $-1$ to encourage the

agent to find the shortest path.

Using Q$-$learning, calculate the Q$-$values for each state$-$action pair after a few iterations $(4-5$

iterations$)$ Assume a discount factor $($ of $0\mathrm{.}9$ and a learning rate $()$ of $0\mathrm{.}1.$