E(\frac{\hat{\partial J}} {\partial \theta}) = E_1[E_2(\frac{\hat{\partial J}} {\partial \theta})] \ &\= E_1[E_2( \frac{1}{K} \sum_{k=1}^{K} \frac{\hat{\partial J_k}} {\partial \theta} )] = E_1[ \frac{1}{K} \sum_{k=1}^{K} E_2(\frac{\hat{\partial J_k}} {\partial \theta}) ] = E_1[ \frac{1}{K} \sum_{k=1}^{K} \frac{\partial J_k} {\partial \theta} ] = \frac{\partial J} {\partial \theta}

这是一个数学公式，描述了期望值的运算性质。在LaTeX中，你可以使用数学环境（如equation、align等）来排版这个公式。以下是你给出的公式的LaTeX代码：

\begin{align*}
E\left(\frac{\hat{\partial J}}{\partial \theta}\right) &= E_1\left[E_2\left(\frac{\hat{\partial J}}{\partial \theta}\right)\right] \\
&= E_1\left[E_2\left(\frac{1}{K} \sum_{k=1}^{K} \frac{\hat{\partial J_k}}{\partial \theta}\right)\right] \\
&= E_1\left[\frac{1}{K} \sum_{k=1}^{K} E_2\left(\frac{\hat{\partial J_k}}{\partial \theta}\right)\right] \\
&= E_1\left[\frac{1}{K} \sum_{k=1}^{K} \frac{\partial J_k}{\partial \theta}\right] \\
&= \frac{\partial J}{\partial \theta}
\end{align*}

希望这可以帮助你。如果你还有其他问题，请随时提问。