# A Reinforcement Learning Approach to Domain-Knowledge Inclusion Using Grammar Guided Symbolic Regression

arXiv: https://arxiv.org/abs/2202.04367 · HTML: https://mlsanity.com/paper/2202.04367/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 63 references that are in the map.
- First posted on arXiv 9 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Programmatically Interpretable Reinforcement Learning](https://mlsanity.com/paper/1804.02477/) (2018)
- [A Closer Look at Invalid Action Masking in Policy Gradient Algorithms](https://mlsanity.com/paper/2006.14171/) (2020)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Feature Engineering for Predictive Modeling using Reinforcement Learning](https://mlsanity.com/paper/1709.07150/) (2017)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Interpretable Policies for Reinforcement Learning by Genetic Programming](https://mlsanity.com/paper/1712.04170/) (2017)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [Beyond variance reduction: Understanding the true impact of baselines on policy optimization](https://mlsanity.com/paper/2008.13773/) (2020)
- [Feature-Based Aggregation and Deep Reinforcement Learning: A Survey and Some New Implementations](https://mlsanity.com/paper/1804.04577/) (2018)
- [Consistent Feature Construction with Constrained Genetic Programming for Experimental Physics](https://mlsanity.com/paper/1908.08005/) (2019)
- [A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems](https://mlsanity.com/paper/1704.00828/) (2017)

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

- [Neuro-Symbolic ODE Discovery with Latent Grammar Flow](https://mlsanity.com/paper/2604.16232/) (2026)
- [Symbolic Density Estimation for Discrete Distributions](https://mlsanity.com/paper/2605.21813/) (2026)

## Abstract (arXiv)

In recent years, symbolic regression has been of wide interest to provide an interpretable symbolic representation of potentially large data relationships. Initially circled to genetic algorithms, symbolic regression methods now include a variety of Deep Learning based alternatives. However, these methods still do not generalize well to real-world data, mainly because they hardly include domain knowledge nor consider physical relationships between variables such as known equations and units. Regarding these issues, we propose a Reinforcement-Based Grammar-Guided Symbolic Regression (RBG2-SR) method that constrains the representational space with domain-knowledge using context-free grammar as reinforcement action space. We detail a Partially-Observable Markov Decision Process (POMDP) modeling of the problem and benchmark our approach against state-of-the-art methods. We also analyze the POMDP state definition and propose a physical equation search use case on which we compare our approach to grammar-based and non-grammarbased symbolic regression methods. The experiment results show that our method is competitive against other state-of-the-art methods on the benchmarks and offers the best error-complexity trade-off, highlighting the interest of using a grammar-based method in a real-world scenario.