deepQ Learning

This question has Latex syntax. Let $r_s \in \{-4,-1,0,1\}$. Starting in \textbf{square 3}, for each of the possible values of $r_s$ briefly explain what the optimal policy would be in Flappy World 2. Using the value of $r_s$, that would cause the optimal policy to return the shortest path to the green target square, find the optimal value function for each square in Flappy world 2. What is the optimal action from square 27?

 

It seems like you're describing a problem related to reinforcement learning and Flappy World 2, possibly using a grid world representation. To address your question, I'll provide a general guide on how to approach this type of problem.

1. Define the State Space:
   • Identify the states in your Flappy World 2. In your case, it seems like there are squares, and you've mentioned "square 3" and "square 27." Clarify what each square represents in terms of the environment.
2. Define the Action Space:
   • Determine the possible actions that the agent can take in each state. For Flappy World 2, actions might include moving up, moving down, or staying in the current position.
3. Define the Reward Function:
   • Specify the rewards associated with different state-action pairs. You've mentioned $r_s \in {-4, -1, 0, 1}$, so there seems to be a reward associated with each state.
4. Define the Transition Model:
   • Determine the probabilities of transitioning from one state to another based on the chosen action. This is often represented by a transition probability matrix.
5. Policy Explanation:
   • For each possible value of $r_s$, explain what the optimal policy would be in Flappy World 2. This involves describing the action that the agent should take in each state to maximize its expected cumulative reward.
6. Optimal Value Function:
   • Calculate the optimal value function for each square in Flappy World 2. This involves finding the expected cumulative reward of following the optimal policy from each state.
7. Optimal Action from Square 27:
   • Determine the optimal action from square 27 based on the calculated optimal value function. This action corresponds to the one that leads to the shortest path to the green target square, considering the value of $r_s$.
8. Implementation:
   • If you have access to reinforcement learning libraries or algorithms, you can implement them to find the optimal policy and value function. Popular methods include Q-learning, SARSA, or deep reinforcement learning algorithms like Deep Q-Networks (DQN).

Remember that the specifics of your problem might require adjustments to these general steps. Additionally, without more details about the environment, rewards, and transitions, it's challenging to provide a more specific solution.