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

TL;DR

This paper introduces RBG2-SR, a reinforcement learning method that incorporates domain knowledge via grammar constraints into symbolic regression, improving interpretability and performance on real-world data.

Contribution

It proposes a novel POMDP-based framework for grammar-guided symbolic regression that effectively integrates domain knowledge and physical relationships.

Findings

Competitive performance against state-of-the-art methods

Best error-complexity trade-off in experiments

Effective use of grammar constraints in real-world scenarios

Abstract

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.