test

docs/10.md

@@ -153,4 +153,16 @@ $$
 
 $$
 = \mathbb{E}_ {s_{0:t},a_{0:(t-1)}} [\mathbb{E}_ {s_{(t+1):T},a_{t:(T-1)}} [\nabla_{\theta}\log \pi_{\theta}(a_t|s_t)b(s_t)]]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}} [b(s_t) \mathbb{E}_ {s_{(t+1):T},a_{t:(T-1)}}[\nabla_{\theta}\log \pi_{\theta}(a_t|s_t)]]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}} [b(s_t) \mathbb{E}_{a_t}[\nabla_{\theta}\log \pi_{\theta}(a_t|s_t)]]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}} [b(s_t) \cdot 0] = 0。
 $$
\ No newline at end of file