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In recent years, symbolic regression has been of wide interest to provide aninterpretable symbolic representation of potentially large data relationships.Initially circled to genetic algorithms, symbolic regression methods nowinclude a variety of Deep Learning based alternatives. However, these methodsstill do not generalize well to real-world data, mainly because they hardlyinclude domain knowledge nor consider physical relationships between variablessuch as known equations and units. Regarding these issues, we propose aReinforcement-Based Grammar-Guided Symbolic Regression (RBG2-SR) method thatconstrains the representational space with domain-knowledge using context-freegrammar as reinforcement action space. We detail a Partially-Observable MarkovDecision Process (POMDP) modeling of the problem and benchmark our approachagainst state-of-the-art methods. We also analyze the POMDP state definitionand propose a physical equation search use case on which we compare ourapproach to grammar-based and non-grammarbased symbolic regression methods. Theexperiment results show that our method is competitive against otherstate-of-the-art methods on the benchmarks and offers the best error-complexitytrade-off, highlighting the interest of using a grammar-based method in areal-world scenario.

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