Difference Between Policy Iteration and Value Iteration

In reinforcement learning and dynamic programming, finding the optimal policy in a Markov Decision Process (MDP) often boils down to two classic algorithms: Policy Iteration and Value Iteration. Both reliably find the optimal strategy, but they differ in how efficiently and quickly they get there.

How Each Algorithm Works

Policy Iteration

1. Policy Evaluation: Estimate the value function Vπ(s)V^\pi(s)Vπ(s) for the current policy by solving Bellman’s expectation equation until it converges.

2. Policy Improvement: Update the policy to be greedy with respect to the evaluated Vπ(s)V^\pi(s)Vπ(s).

3. Repeat these steps until the policy no longer changes

Value Iteration

• Combines evaluation and improvement in each sweep.

• Computes the optimal value function directly using Bellman’s optimality equation:

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• After convergence, derives the optimal policy via a greedy step.

Quick Comparison Table

Pros & Cons

Value Iteration

• Simpler to implement

• Good for moderate MDPs
  – May need many iterations; each iteration computes maxima over all actions

Policy Iteration

• Converges in fewer stepsMore stable policy updates
  – Each iteration requires full policy evaluation (solving linear equations or iterative sweeps)

🏁 Which One Should You Use?

• For small to medium MDPs where convergence speed is key, Policy Iteration is often more efficient: fewer iterations, faster policy refinement.

• For larger or simpler problems with limited computational budget per step, Value Iteration may be more practical.

Hybrid Approaches Exist

Algorithms like Modified Policy Iteration stop evaluation early, offering a middle ground—trading off between the speed of value updates and the efficiency of policy iteration

✅ Final Recommendation

If you’re optimizing for faster convergence and stability, start with Policy Iteration. If you want simplicity and lower per-step cost, go with Value Iteration, especially on moderate-sized problems.