Value Iteration is different from policy iteration . It updates the value function using the Bellman Optimality Equation...
Pankaj
February 14, 2024
Given an understanding of policy iteration and truncated policy iteration, how does value iteration work? Can you first outline the algorithm step by step, differentiate it from policy iteration, and then provide a comprehensive example?🔗
Policy Iteration alternates between two distinct steps: Policy Evaluation (where the value function for a given policy is computed to convergence) and Policy Improvement (where the policy is updated based on the value function).
Value Iteration compresses these two steps into one. It updates the value function using the Bellman Optimality Equation, and this process implicitly defines the policy at each step. Only after the value function converges is the optimal policy explicitly extracted.
While Policy Iteration fully evaluates a policy before improving it, Value Iteration constantly improves its value estimates and implicitly its policy in each iteration.
The value remains 0 as all actions have the same value.
For the cell next to G (bottom-center):
Best move is Right towards G: V=−1+10=9
After several iterations, the value of each cell will reflect the maximum expected reward from that position.
Policy Extraction: The robot will choose actions based on the maximum expected value of adjacent cells. For instance, in the cell next to G, the best action is to move right, towards G.
With Value Iteration, the robot iteratively refines its value estimates for each cell in the maze until they converge. Once converged, the robot can then determine the optimal action in each cell to reach the goal efficiently. The primary difference from Policy Iteration is that the robot doesn't work with an explicit policy during the iteration process, only extracting it at the end.
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