test

docs/8&9.md

@@ -394,5 +394,25 @@ $$
 $$
 
 $$
-= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \sum_a \pi_{\theta}(a_t|s_t)\frac{\nabla_{\theta}\pi_{\theta}(a_t|s_t)}{\pi_{\theta}(a_t|s_t)}] \quad \text{（将期望展开 + test对数函数求导）}
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \sum_{a_t} \pi_{\theta}(a_t|s_t)\frac{\nabla_{\theta}\pi_{\theta}(a_t|s_t)}{\pi_{\theta}(a_t|s_t)}] \quad \text{（将期望展开 + 对数函数求导）}
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \sum_{a_t} \nabla_{\theta}\pi_{\theta}(a_t|s_t)]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \nabla_{\theta} \sum_{a_t} \pi_{\theta}(a_t|s_t)]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \nabla_{\theta} 1]
+$$
+
+$$
+= \mathbb{E}_ {s_{0:t},a_{0:(t-1)}}[b(s_t) \cdot 0]
+$$
+
+$$
+= 0。
 $$
\ No newline at end of file