# How can the policy iteration algorithm be model-free if it uses the transition probabilities?

I'm actually trying to understand the policy iteration in the context of RL. I read an article presenting it and, at some point, a pseudo-code of the algorithm is given :

What I can't understand is this line :

From what I understand, policy iteration is a model-free algorithm, which means that it doesn't need to know the environment's dynamics. But, in this line, we need $$p(s',r \mid s, \pi(s))$$ (which in my understanding is the transition function of the MDP that gave us the probability of landing in the state $$s'$$ knowing previous $$s$$ state and the action taken) to compute $$V(s)$$. So I don't understand how we can compute $$V(s)$$ with the quantity $$p(s',r \mid s, \pi(s))$$ since it is a parameter of the environment.

## 2 Answers

Everything you say in your post is correct, apart from the wrong assumption that policy iteration is model-free. PI is a model-based algorithm because of the reasons you're mentioning.

The Policy Iteration algorithm (given in the question) is model-based.

However, note that there exist methods that fall into the Generalized Policy Iteration category, such as SARSA, which are model-free.

From what I understand, policy iteration is a model-free algorithm

Maybe this was referring to generalized policy iteration methods.

(Answer based on comments from @Neil Slater.)

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– nbro
Oct 21 '21 at 12:59