Neural Math Word Problem Solver with Reinforcement Learning

Danqing Huang, Jing Liu, Chin-Yew Lin, Jian Yin


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.
Anthology ID:
C18-1018
Volume:
Proceedings of the 27th International Conference on Computational Linguistics
Month:
August
Year:
2018
Address:
Santa Fe, New Mexico, USA
Venue:
COLING
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
213–223
Language:
URL:
https://www.aclweb.org/anthology/C18-1018
DOI:
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PDF:
http://aclanthology.lst.uni-saarland.de/C18-1018.pdf