@InProceedings{huang-EtAl:2018:C18-1,
  author    = {Huang, Danqing  and  Liu, Jing  and  Lin, Chin-Yew  and  Yin, Jian},
  title     = {Neural Math Word Problem Solver with Reinforcement Learning},
  booktitle = {Proceedings of the 27th International Conference on Computational Linguistics},
  month     = {August},
  year      = {2018},
  address   = {Santa Fe, New Mexico, USA},
  publisher = {Association for Computational Linguistics},
  pages     = {213--223},
  abstract  = {Sequence-to-sequence model has been applied to solve math word problems. The model takes math problem descriptions as input and generates equations as output. The advantage of sequence-to-sequence model requires no feature engineering and can generate equations that do not exist in training data. However, our experimental analysis reveals that this model suffers from two shortcomings: (1) generate spurious numbers; (2) generate numbers at wrong positions. In this paper, we propose incorporating copy and alignment mechanism to the sequence-to-sequence model (namely CASS) to address these shortcomings. To train our model, we apply reinforcement learning to directly optimize the solution accuracy. It overcomes the ``train-test discrepancy'' issue of maximum likelihood estimation, which uses the surrogate objective of maximizing equation likelihood during training while the evaluation metric is solution accuracy (non-differentiable) at test time. Furthermore, to explore the effectiveness of our neural model, we use our model output as a feature and incorporate it into the feature-based model. Experimental results show that (1) The copy and alignment mechanism is effective to address the two issues; (2) Reinforcement learning leads to better performance than maximum likelihood on this task; (3) Our neural model is complementary to the feature-based model and their combination significantly outperforms the state-of-the-art results.},
  url       = {http://www.aclweb.org/anthology/C18-1018}
}