Merge pull request #503 from huggingface/ThomasSimonini/UpdateUnit4

Update pg-theorem.mdx

Author: simoninithomas

units/en/unit4/pg-theorem.mdx

@@ -27,9 +27,13 @@ We then multiply every term in the sum by \\(\frac{P(\tau;\theta)}{P(\tau;\theta
 
 \\( = \sum_{\tau} \frac{P(\tau;\theta)}{P(\tau;\theta)}\nabla_\theta P(\tau;\theta)R(\tau) \\)
 
-We can simplify further this since \\( \frac{P(\tau;\theta)}{P(\tau;\theta)}\nabla_\theta P(\tau;\theta) =  P(\tau;\theta)\frac{\nabla_\theta P(\tau;\theta)}{P(\tau;\theta)}  \\)
+We can simplify further this since 
 
-\\(= \sum_{\tau} P(\tau;\theta) \frac{\nabla_\theta P(\tau;\theta)}{P(\tau;\theta)}R(\tau) \\)
+\\( \frac{P(\tau;\theta)}{P(\tau;\theta)}\nabla_\theta P(\tau;\theta) =  P(\tau;\theta)\frac{\nabla_\theta P(\tau;\theta)}{P(\tau;\theta)} \\)
+
+
+
+\\( P(\tau;\theta)\frac{\nabla_\theta P(\tau;\theta)}{P(\tau;\theta)}= \sum_{\tau} P(\tau;\theta) \frac{\nabla_\theta P(\tau;\theta)}{P(\tau;\theta)}R(\tau) \\)
 
 We can then use the *derivative log trick* (also called *likelihood ratio trick* or *REINFORCE trick*), a simple rule in calculus that implies that \\( \nabla_x log f(x) = \frac{\nabla_x f(x)}{f(x)} \\)