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Mathematical reasoning, a core ability of human intelligence, presents uniquechallenges for machines in abstract thinking and logical reasoning. Recentlarge pre-trained language models such as GPT-3 have achieved remarkableprogress on mathematical reasoning tasks written in text form, such as mathword problems (MWP). However, it is unknown if the models can handle morecomplex problems that involve math reasoning over heterogeneous information,such as tabular data. To fill the gap, we present Tabular Math Word Problems(TabMWP), a new dataset containing 38,431 open-domain grade-level problems thatrequire mathematical reasoning on both textual and tabular data. Each questionin TabMWP is aligned with a tabular context, which is presented as an image,semi-structured text, and a structured table. There are two types of questions:free-text and multi-choice, and each problem is annotated with gold solutionsto reveal the multi-step reasoning process. We evaluate different pre-trainedmodels on TabMWP, including the GPT-3 model in a few-shot setting. As earlierstudies suggest, since few-shot GPT-3 relies on the selection of in-contextexamples, its performance is unstable and can degrade to near chance. Theunstable issue is more severe when handling complex problems like TabMWP. Tomitigate this, we further propose a novel approach, PromptPG, which utilizespolicy gradient to learn to select in-context examples from a small amount oftraining data and then constructs the corresponding prompt for the testexample. Experimental results show that our method outperforms the bestbaseline by 5.31% on the accuracy metric and reduces the prediction variancesignificantly compared to random selection, which verifies its effectiveness inselecting in-context examples.

Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning