# A Reinforcement Learning Environment for Mathematical Reasoning via Program Synthesis

arXiv: https://arxiv.org/abs/2107.07373 · HTML: https://mlsanity.com/paper/2107.07373/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Neural Module Networks for Reasoning over Text](https://mlsanity.com/paper/1912.04971/) (2019)
- [Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension](https://mlsanity.com/paper/1909.00109/) (2019)
- [Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving](https://mlsanity.com/paper/1910.06611/) (2019)

## Built on by (most cited first, 2 of 2)

- [Teaching Autoregressive Language Models Complex Tasks By Demonstration](https://mlsanity.com/paper/2109.02102/) (2021)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)

## Abstract (arXiv)

We convert the DeepMind Mathematics Dataset into a reinforcement learning environment by interpreting it as a program synthesis problem. Each action taken in the environment adds an operator or an input into a discrete compute graph. Graphs which compute correct answers yield positive reward, enabling the optimization of a policy to construct compute graphs conditioned on problem statements. Baseline models are trained using Double DQN on various subsets of problem types, demonstrating the capability to learn to correctly construct graphs despite the challenges of combinatorial explosion and noisy rewards.