Difference Between Policy Iteration and Value Iteration

In reinforcement learning, two common methods for solving Markov Decision Processes (MDPs) are policy iteration and value iteration. Both approaches are used to find the optimal policy, but they differ in how they update values and policies. Let’s explore the difference between policy iteration and value iteration.

What Is Policy Iteration?

Policy iteration is an iterative process that alternates between policy evaluation and policy improvement to find the optimal policy.

1. Policy Evaluation:
   In this step, the algorithm evaluates a given policy by calculating the value function for each state under that policy. It computes how good it is to be in a particular state when following the current policy.

2. Policy Improvement:
   Once the value function is computed, the policy is updated to make better decisions in each state. The algorithm improves the policy by choosing actions that maximize the value function in each state.

The algorithm keeps alternating between policy evaluation and policy improvement until the policy converges to the optimal policy.

What Is Value Iteration?

Value iteration simplifies the process by combining policy evaluation and improvement into a single step. Instead of fully evaluating a policy, value iteration focuses on improving the value function at each step.

1. Value Update:
   Value iteration updates the value function by iteratively applying the Bellman equation. For each state, it computes the maximum expected value of future rewards based on the available actions.

2. Policy Extraction:
   Once the value function is sufficiently accurate, the optimal policy is extracted by choosing the actions that maximize the value function in each state.

The key difference is that value iteration updates both the values and the policy at the same time, speeding up convergence compared to policy iteration.

Key Differences

Here is a summary of the main differences between policy iteration and value iteration:

The difference between policy iteration and value iteration lies in their approach to finding the optimal policy. Policy iteration alternates between policy evaluation and improvement, while value iteration focuses on updating value functions directly. Both methods aim to optimize decision-making in uncertain environments but are suited for different types of problems.