Policy and Value Iteration

Step-by-Step Tutorial: Understanding Policy and Value Iteration

1. Introduction to Value Iteration:

• Value Iteration is an algorithm used to solve Markov Decision Processes (MDPs) by finding the optimal policies when the true transition probabilities and reward functions are known.
• The algorithm is based on the Bellman Equation, which defines the optimal value function.

2. Value Iteration Algorithm:

• Start by setting the initial values of all states to zero.
• Iteratively compute the value function using dynamic programming.
• Update the value function at each iteration using the Bellman update rule.
• Repeat the process until the value function converges to the optimal value function.

3. Applying Value Iteration to Grid World MDP:

• Consider a Grid World MDP with terminal states and transition probabilities.
• Initialize the estimate of the optimal value function to zeros.
• Use the Bellman update rule to compute the value function iteratively for each state.
• Update the values based on the rewards and transition probabilities.
• Continue iterating until the values converge for all states.

4. Policy Iteration:

• Policy Iteration is an alternative approach to Value Iteration.
• It involves two steps: policy evaluation and policy improvement.
• Evaluate the value function corresponding to the current policy.
• Improve the policy by selecting the best action based on the evaluated value function.
• Repeat the process until convergence to find the optimal policy.

5. Relationship between Value Iteration and Policy Iteration:

• Policy Iteration can be seen as a combination of policy evaluation and policy improvement steps.
• The algorithm aims to find the optimal policy by iteratively evaluating and improving policies.
• Policy Iteration can be proven to be optimal under certain conditions.

6. Hybrid Methods:

• Hybrid methods exist that combine aspects of both Value Iteration and Policy Iteration.
• These methods offer flexibility in finding solutions to MDPs based on the specific problem requirements.
• Depending on the scenario, different methods may be more suitable for solving MDPs efficiently.

By following these steps, you can gain a comprehensive understanding of Policy and Value Iteration algorithms for solving Markov Decision Processes.