  Discovering the underlying mathematical expressions describing a dataset is a
core challenge for artificial intelligence. This is the problem of
$\textit{symbolic regression}$. Despite recent advances in training neural
networks to solve complex tasks, deep learning approaches to symbolic
regression are underexplored. We propose a framework that leverages deep
learning for symbolic regression via a simple idea: use a large model to search
the space of small models. Specifically, we use a recurrent neural network to
emit a distribution over tractable mathematical expressions and employ a novel
risk-seeking policy gradient to train the network to generate better-fitting
expressions. Our algorithm outperforms several baseline methods (including
Eureqa, the gold standard for symbolic regression) in its ability to exactly
recover symbolic expressions on a series of benchmark problems, both with and
without added noise. More broadly, our contributions include a framework that
can be applied to optimize hierarchical, variable-length objects under a
black-box performance metric, with the ability to incorporate constraints in
situ, and a risk-seeking policy gradient formulation that optimizes for
best-case performance instead of expected performance.
