GFN-SR: Symbolic Regression with Generative Flow Networks
Sida Li Ioana Marinescu Sebastian Musslick
Symbolic regression (SR) is an area of interpretable machine learning that
aims to identify mathematical expressions, often composed of simple functions,
that best fit in a given set of covariates $X$ and response $y$. In recent
years, deep symbolic regression (DSR) has emerged as a popular method in the
field by leveraging deep reinforcement learning to solve the complicated
combinatorial search problem. In this work, we propose an alternative framework
(GFN-SR) to approach SR with deep learning. We model the construction of an
expression tree as traversing through a directed acyclic graph (DAG) so that
GFlowNet can learn a stochastic policy to generate such trees sequentially.
Enhanced with an adaptive reward baseline, our method is capable of generating
a diverse set of best-fitting expressions. Notably, we observe that GFN-SR
outperforms other SR algorithms in noisy data regimes, owing to its ability to
learn a distribution of rewards over a space of candidate solutions.