[QUESTION] How P(τ;θ) disappeared while estimating the gradients using trajectory samples?

[ritwikmishra]

I am referring to the gradient derivation here.

The paragraph where the instructor claimed "we can approximate the likelihood ratio policy gradient with sample-based estimate" then term of P(τ;θ) (probability of trajectory τ given the parameters θ) disappeared in the subsequent summation. Why?

I asked the same question on the discord study-group (here) but got no response.

[simoninithomas]

Hey there 👋

So P(tau;theta) is The probability of a trajectory but we can't have it. Since it would imply to know the environment dynamics (state dist)

If you look at the formulas after what we do is:

• Replace P(τ;θ) (impossible to calculate)
• With
  
  where tau(i) is a sampled trajectory

Don't hesitate to take a piece of paper and write each part step by step to understand better. It's how I've did it.

[ritwikmishra]

@simoninithomas
I am sorry but it is still unclear to me. My doubt is... how we jumped from this

to this

shouldn't it be as follows: