test

docs/8&9.md

@@ -337,4 +337,12 @@ $$
 
 $$
 = \phi(s,a) - \sum_{a'} \phi(s,a') \frac{e^{\phi(s,a')^{\text{T}}\theta}}{\sum_{a''}e^{\phi(s,a'')^{\text{T}}\theta}}
+$$
+
+$$
+= \phi(s,a) - \sum_{a'} \phi(s,a') \pi_{\theta}(a'|s)
+$$
+
+$$
+= \phi(s,a) - \mathbb{E}_ {a'\sim\pi_{\theta}(a'|s)}[\phi(s,a')]
 $$
\ No newline at end of file