question words, and it can be optimized in an end-to-end manner by back-propagation. Given the input fact $F$, additional textual context $C$ and target question word sequence $Y$, the object function is to optimize the following negative log-likelihood:$$\begin{split}
\mathcal{L}_{ques\_loss}\!=\!\frac{-1}{|Y|}\! \sum _{t=1}^{|Y|} \! {\rm log}[P(y_t|\textbf{s}_t,\!y_{t-1},\!F,\!C)]
\end{split}
\label{eq:ques_loss}$$

The question-aware loss $\mathcal{L}_{ques\_loss}$ does not require any additional labels to optimize because the three modes share a same ${\rm softmax}$ classifier to keep a balance (Equation \[eq:mode\]), and they can learn to coordinate each other by minimizing $\mathcal{L}_{ques\_loss}$.

### Answer-Aware loss {#subsubsec:ans_loss}

It is able to generate questions similar to the labeled questions by optimizing the question-aware loss $\mathcal{L}_{ques\_loss}$. However, there is an ambiguous problem in the annotated questions where the questions have alternative answers rather than determinate answers [@D18-1051]. In order to make generated questions correspond to definitive answers, we propose a novel answer-aware loss. By answer-aware loss, we aim at generating an answer type word in the question, which contributes to generating a question word matching the answer type. Formally, the answer-aware loss is in the following: $$\begin{split}
\mathcal{L}_{ans\_loss}=\underset{a_n,a_n \in A}{{\rm min}} \ \ \underset{y_t,y_t \in Y}{{\rm min}} \ H_{a_n,y_t}
\end{split}
\label{eq:ans_loss}$$ where $A=\{a_n\}_{n=1}^{|A|}$ is a set of answer type words. 