  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.
